CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SCT171+6 : TPTP v9.2.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n010.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 05:06:20 PM UTC 2026

% Result   : Theorem 1.91s 1.85s
% Output   : CNFRefutation 1.98s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_839)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_44__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_46_notin__Lin__iff,axiom,
    ! [X6,X7,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
       => ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8))
        <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X7),X6)),X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_notin__Lin__iff) ).

fof(fact_122_linorder__antisym__conv2,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_linorder__antisym__conv2) ).

fof(fact_69_linorder__antisym__conv3,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X7,X6] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_linorder__antisym__conv3) ).

fof(fact_117_linorder__antisym__conv1,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_linorder__antisym__conv1) ).

fof(fact_160_linorder__neqE__linordered__idom,axiom,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X33,X34] :
          ( ti(X3,X33) != ti(X3,X34)
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_linorder__neqE__linordered__idom) ).

fof(fact_71_not__less__iff__gr__or__eq,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
            | ti(X3,X6) = ti(X3,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_not__less__iff__gr__or__eq) ).

fof(fact_68_linorder__neqE,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ti(X3,X33) != ti(X3,X34)
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_linorder__neqE) ).

fof(fact_52_linorder__cases,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( ti(X3,X33) != ti(X3,X34)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_linorder__cases) ).

fof(fact_196_equalityE,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => ~ ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
         => ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_equalityE) ).

fof(help_fequal_1_1_T,axiom,
    ! [X3,X33,X34] :
      ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X33),X34))
      | ti(X3,X33) = ti(X3,X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).

fof(fact_92__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O,axiom,
    ~ ! [X44] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
       => ( ! [X32] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X44))
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) )
         => ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X44),one_one(nat))))),lab)),lba)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O) ).

fof(fact_435_card__less__Suc2,axiom,
    ! [X42,X71] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_card__less__Suc2) ).

fof(fact_6__C2_C,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X13)
         => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X12)
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
               => ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__C2_C) ).

fof(help_COMBI_1_1_U,axiom,
    ! [X3,X86] : hAPP(X3,X3,combi(X3),X86) = ti(X3,X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).

fof(fact_7__C1_C,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X13)
         => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X12)
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
               => ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                   => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C1_C) ).

fof(fact_9_pairwise__neutrality,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
         => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
           => ( ! [X16] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
             => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).

fof(fact_82__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
    ! [X16] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)))
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) ) ),
    file('/export/starexec/sandbox2/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_8__C4_C,axiom,
    ! [X10,X11,X17,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X17)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X17)
         => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
             => ( ! [X16] :
                    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X17)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
               => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X17)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C4_C) ).

fof(fact_85_dictatorI,axiom,
    ! [X42,X25] :
      ( hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X25),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
     => ( ! [X26] :
            ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
           => ! [X19,X20] :
                ( ti(arrow_490897120le_alt,X19) != ti(arrow_490897120le_alt,X20)
               => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X42)))
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26))) ) ) )
       => hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X25),X42)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_dictatorI) ).

fof(fact_10__C3_C,axiom,
    ! [X10,X11,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
       => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
         => ( ! [X16] :
                ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
           => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
            <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C3_C) ).

fof(fact_217_in__below,axiom,
    ! [X6,X7,X8,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X8),X14),X15)))
        <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
            & ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X14)
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X15)),X8)) )
            & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X14)
             => ( ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X14)
                 => ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X15)
                    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X7)),X8)) ) )
                & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X14)
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_in__below) ).

fof(fact_78_in__above,axiom,
    ! [X6,X7,X8,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X8),X14),X15)))
        <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
            & ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X15)
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X7)),X8)) )
            & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X15)
             => ( ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X15)
                 => ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X14)
                    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X14)),X8)) ) )
                & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X15)
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_in__above) ).

fof(fact_79_pred__equals__eq2,axiom,
    ! [X3,X1,X40,X41] :
      ( ! [X26,X27] :
          ( hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X26),X27)),X41))
        <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X26),X27)),X40)) )
    <=> ti(fun(product_prod(X3,X1),bool),X41) = ti(fun(product_prod(X3,X1),bool),X40) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_pred__equals__eq2) ).

fof(fact_305_folding__image__simple__idem_Oidem,axiom,
    ! [X1,X3,X6,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,X6),X6) = ti(X3,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_folding__image__simple__idem_Oidem) ).

fof(fact_238_below__Lin,axiom,
    ! [X8,X6,X7] :
      ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X8),X6),X7)),arrow_2064824852le_Lin)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_below__Lin) ).

fof(fact_50_above__Lin,axiom,
    ! [X8,X6,X7] :
      ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X8),X6),X7)),arrow_2064824852le_Lin)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_above__Lin) ).

fof(fact_472_pigeonhole,axiom,
    ! [X3,X1,X37,X39] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39))),hAPP(fun(X1,bool),nat,finite_card(X1),X39)))
     => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X37),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_pigeonhole) ).

fof(fact_47_Lin__irrefl,axiom,
    ! [X14,X15,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X8))
       => ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),X8)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Lin__irrefl) ).

fof(fact_4_in__mkbot,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X8),X9)))
    <=> ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X9)
        & ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X9)
         => ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7) )
        & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X9)
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_in__mkbot) ).

fof(fact_5_in__mktop,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X8),X9)))
    <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X9)
        & ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X9)
         => ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7) )
        & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X9)
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__mktop) ).

fof(fact_477_inv__into__injective,axiom,
    ! [X1,X3,X39,X37,X6,X7] :
      ( hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X6) = hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X7)
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)))
         => ti(X1,X6) = ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_inv__into__injective) ).

fof(fact_465_endo__inj__surj,axiom,
    ! [X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39)),X39))
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),X39))
         => hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39) = ti(fun(X3,bool),X39) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_endo__inj__surj) ).

fof(fact_86_PiE,axiom,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
     => ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,fun(X1,bool),X43,X6)))
       => ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_PiE) ).

fof(fact_496_image__surj__f__inv__f,axiom,
    ! [X1,X3,X39,X37] :
      ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))) = top_top(fun(X3,bool))
     => hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),top_top(fun(X1,bool))),X37)),X39)) = ti(fun(X3,bool),X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_image__surj__f__inv__f) ).

fof(fact_479_f__inv__into__f,axiom,
    ! [X3,X1,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
     => hAPP(X1,X3,X37,hAPP(X3,X1,hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),X39),X37),X7)) = ti(X3,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_f__inv__into__f) ).

fof(fact_485_subset__image__iff,axiom,
    ! [X3,X1,X43,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
    <=> ? [X81] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X81),X39))
          & ti(fun(X3,bool),X43) = hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X81) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_subset__image__iff) ).

fof(fact_218_add__leE,axiom,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__leE) ).

fof(fact_482_image__iff,axiom,
    ! [X3,X1,X9,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X9),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
    <=> ? [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X39))
          & ti(X3,X9) = hAPP(X1,X3,X37,X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_image__iff) ).

fof(fact_300_card__seteq,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X43)),hAPP(fun(X3,bool),nat,finite_card(X3),X39)))
         => ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_card__seteq) ).

fof(fact_240_not__add__less1,axiom,
    ! [X58,X59] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_not__add__less1) ).

fof(fact_241_not__add__less2,axiom,
    ! [X59,X58] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X58)),X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_not__add__less2) ).

fof(fact_455_card__def,axiom,
    ! [X3,X39] :
      ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,hAPP(nat,fun(fun(X3,bool),nat),hAPP(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat))),finite_fold_image(nat,X3),plus_plus(nat)),hAPP(nat,fun(X3,nat),combk(nat,X3),one_one(nat))),zero_zero(nat)),X39) )
      & ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_card__def) ).

fof(fact_87_complete__Lin,axiom,
    ! [X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ? [X26] :
          ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X26),arrow_2064824852le_Lin))
          & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_complete__Lin) ).

fof(fact_135_inj__on__iff,axiom,
    ! [X3,X1,X7,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
         => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
          <=> ti(X3,X6) = ti(X3,X7) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_inj__on__iff) ).

fof(fact_136_inj__onD,axiom,
    ! [X3,X1,X6,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
           => ti(X3,X6) = ti(X3,X7) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_inj__onD) ).

fof(fact_134_inj__on__contraD,axiom,
    ! [X3,X1,X6,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( ti(X3,X6) != ti(X3,X7)
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
           => hAPP(X3,X1,X37,X6) != hAPP(X3,X1,X37,X7) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_inj__on__contraD) ).

fof(fact_133_inj__on__def,axiom,
    ! [X3,X1,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => ! [X27] :
              ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X27),X39))
             => ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X27)
               => ti(X3,X26) = ti(X3,X27) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_inj__on__def) ).

fof(fact_458_image__eqI,axiom,
    ! [X3,X1,X39,X15,X37,X6] :
      ( ti(X3,X15) = hAPP(X1,X3,X37,X6)
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_image__eqI) ).

fof(fact_480_rev__image__eqI,axiom,
    ! [X1,X3,X15,X37,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => ( ti(X1,X15) = hAPP(X3,X1,X37,X6)
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_rev__image__eqI) ).

fof(fact_43__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [X31] :
        ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),X31))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X31),arrow_2064824852le_Lin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

fof(fact_42__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [X30] :
        ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),X30))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X30),arrow_2064824852le_Lin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

fof(fact_146_inv__into__f__eq,axiom,
    ! [X3,X1,X7,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => ( hAPP(X3,X1,X37,X6) = ti(X1,X7)
         => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X7) = ti(X3,X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_inv__into__f__eq) ).

fof(fact_145_inv__into__f__f,axiom,
    ! [X3,X1,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),hAPP(X3,X1,X37,X6)) = ti(X3,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_inv__into__f__f) ).

fof(fact_148_inj__imp__inv__eq,axiom,
    ! [X3,X1,X38,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( ! [X26] : hAPP(X3,X1,X37,hAPP(X1,X3,X38,X26)) = ti(X1,X26)
       => hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37) = ti(fun(X1,X3),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_inj__imp__inv__eq) ).

fof(fact_487_atLeastLessThan__eq__iff,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X17,X79,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
           => ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
            <=> ( ti(X3,X14) = ti(X3,X17)
                & ti(X3,X15) = ti(X3,X79) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_atLeastLessThan__eq__iff) ).

fof(fact_488_atLeastLessThan__inj_I1_J,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
           => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
             => ti(X3,X14) = ti(X3,X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_atLeastLessThan__inj_I1_J) ).

fof(fact_489_atLeastLessThan__inj_I2_J,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
           => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
             => ti(X3,X15) = ti(X3,X79) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_atLeastLessThan__inj_I2_J) ).

fof(fact_378_not__less__eq__eq,axiom,
    ! [X54,X29] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),X54)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_not__less__eq__eq) ).

fof(tsy_c_Finite__Set_Ofolding__image__simple__idem_res,axiom,
    ! [X3,X1] : ti(fun(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)))),finite908156982e_idem(X3,X1)) = finite908156982e_idem(X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple__idem_res) ).

fof(fact_155_less__fun__def,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less(fun(X3,X1)),X37),X38))
        <=> ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
            & ~ hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X38),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_less__fun__def) ).

fof(fact_491_range__eqI,axiom,
    ! [X3,X1,X15,X37,X6] :
      ( ti(X3,X15) = hAPP(X1,X3,X37,X6)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_range__eqI) ).

fof(fact_206_set__eq__subset,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
        & hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_set__eq__subset) ).

fof(fact_188_equalityI,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39))
       => ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_equalityI) ).

fof(fact_83_inv__f__eq,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = ti(X1,X7)
       => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37),X7) = ti(X3,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_inv__f__eq) ).

fof(fact_84_inv__f__f,axiom,
    ! [X3,X1,X6,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37),hAPP(X3,X1,X37,X6)) = ti(X3,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_inv__f__f) ).

fof(fact_342_add__nonneg__eq__0__iff,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X7,X6] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X6))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X7))
           => ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X6),X7) = zero_zero(X3)
            <=> ( ti(X3,X6) = zero_zero(X3)
                & ti(X3,X7) = zero_zero(X3) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_add__nonneg__eq__0__iff) ).

fof(fact_391_not__less__eq,axiom,
    ! [X54,X29] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_not__less__eq) ).

fof(fact_191_subset__iff__psubset__eq,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
        | ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_subset__iff__psubset__eq) ).

fof(fact_190_psubset__eq,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
        & ti(fun(X3,bool),X39) != ti(fun(X3,bool),X43) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_psubset__eq) ).

fof(fact_382_le__SucE,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,suc,X53)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
       => X51 = hAPP(nat,nat,suc,X53) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_le__SucE) ).

fof(fact_113_less__le__not__le,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_less__le__not__le) ).

fof(fact_399_less__SucE,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
       => X51 = X53 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_less__SucE) ).

fof(fact_395_less__antisym,axiom,
    ! [X53,X51] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X51))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,suc,X51)))
       => X51 = X53 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_less__antisym) ).

fof(fact_394_not__less__less__Suc__eq,axiom,
    ! [X29,X54] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54)))
      <=> X29 = X54 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_not__less__less__Suc__eq) ).

fof(fact_106_order__eq__iff,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( ti(X3,X6) = ti(X3,X7)
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_order__eq__iff) ).

fof(fact_103_order__antisym__conv,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X7,X6] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_order__antisym__conv) ).

fof(fact_98_order__antisym,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
           => ti(X3,X33) = ti(X3,X34) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_order__antisym) ).

fof(fact_96_xt1_I5_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
           => ti(X3,X33) = ti(X3,X34) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_xt1_I5_J) ).

fof(fact_377_Suc__n__not__le__n,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X53)),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_Suc__n__not__le__n) ).

fof(fact_366_ex__least__nat__less,axiom,
    ! [X29,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X29))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X29))
            & ! [X16] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X62))
               => ~ hBOOL(hAPP(nat,bool,X11,X16)) )
            & hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),one_one(nat)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_ex__least__nat__less) ).

fof(fact_60_xt1_I9_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_xt1_I9_J) ).

fof(fact_66_order__less__not__sym,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_order__less__not__sym) ).

fof(fact_65_order__less__imp__not__less,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_order__less__imp__not__less) ).

fof(fact_61_order__less__asym_H,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_order__less__asym_H) ).

fof(fact_53_order__less__asym,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_order__less__asym) ).

fof(fact_110_linorder__not__le,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_linorder__not__le) ).

fof(fact_120_leD,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_leD) ).

fof(fact_109_linorder__not__less,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_linorder__not__less) ).

fof(fact_101_xt1_I3_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X21,X22] :
          ( ti(X3,X21) = ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_xt1_I3_J) ).

fof(fact_99_xt1_I4_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
         => ( ti(X3,X22) = ti(X3,X36)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_xt1_I4_J) ).

fof(fact_58_xt1_I1_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X21,X22] :
          ( ti(X3,X21) = ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_xt1_I1_J) ).

fof(fact_56_xt1_I2_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
         => ( ti(X3,X22) = ti(X3,X36)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_xt1_I2_J) ).

fof(fact_125_xt1_I11_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
         => ( ti(X3,X21) != ti(X3,X22)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_xt1_I11_J) ).

fof(fact_124_order__le__neq__trans,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( ti(X3,X21) != ti(X3,X22)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_order__le__neq__trans) ).

fof(fact_123_order__le__imp__less__or__eq,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
            | ti(X3,X33) = ti(X3,X34) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_order__le__imp__less__or__eq) ).

fof(fact_118_order__neq__le__trans,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( ti(X3,X21) != ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_order__neq__le__trans) ).

fof(fact_114_order__le__less,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
            | ti(X3,X6) = ti(X3,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_order__le__less) ).

fof(fact_112_order__less__le,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & ti(X3,X6) != ti(X3,X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_order__less__le) ).

fof(fact_119_xt1_I12_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( ti(X3,X21) != ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_xt1_I12_J) ).

fof(fact_143_inj__eq,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
      <=> ti(X3,X6) = ti(X3,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_inj__eq) ).

fof(fact_144_injD,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
       => ti(X3,X6) = ti(X3,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_injD) ).

fof(fact_368_ex__least__nat__le,axiom,
    ! [X29,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X29))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X29))
            & ! [X16] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X62))
               => ~ hBOOL(hAPP(nat,bool,X11,X16)) )
            & hBOOL(hAPP(nat,bool,X11,X62)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_ex__least__nat__le) ).

fof(fact_301_ex__new__if__finite,axiom,
    ! [X3,X39] :
      ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => ? [X19] : ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X19),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_ex__new__if__finite) ).

fof(fact_473_Ints__double__eq__0__iff,axiom,
    ! [X3] :
      ( ring_char_0(X3)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14) = zero_zero(X3)
          <=> ti(X3,X14) = zero_zero(X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_Ints__double__eq__0__iff) ).

fof(fact_275_inj__onI,axiom,
    ! [X1,X3,X37,X39] :
      ( ! [X26,X46] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X46),X39))
           => ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X46)
             => ti(X3,X26) = ti(X3,X46) ) ) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_inj__onI) ).

fof(tsy_c_Finite__Set_Ofold__image_res,axiom,
    ! [X3] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)))),finite_fold_image(nat,X3)) = finite_fold_image(nat,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofold__image_res) ).

fof(fact_72_linorder__neq__iff,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ti(X3,X6) != ti(X3,X7)
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
            | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_linorder__neq__iff) ).

fof(fact_70_linorder__less__linear,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
          | ti(X3,X33) = ti(X3,X34)
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_linorder__less__linear) ).

fof(fact_22_Pair__eq,axiom,
    ! [X1,X3,X14,X15,X12,X13] :
      ( hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X14),X15) = hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X12),X13)
    <=> ( ti(X3,X14) = ti(X3,X12)
        & ti(X1,X15) = ti(X1,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Pair__eq) ).

fof(fact_21_Pair__inject,axiom,
    ! [X1,X3,X21,X22,X23,X24] :
      ( hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X21),X22) = hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X23),X24)
     => ~ ( ti(X3,X21) = ti(X3,X23)
         => ti(X1,X22) != ti(X1,X24) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Pair__inject) ).

fof(fact_67_less__imp__neq,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X33) != ti(X3,X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__imp__neq) ).

fof(fact_64_order__less__imp__not__eq,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X33) != ti(X3,X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_order__less__imp__not__eq) ).

fof(fact_63_order__less__imp__not__eq2,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X34) != ti(X3,X33) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_order__less__imp__not__eq2) ).

fof(fact_152_injI,axiom,
    ! [X3,X1,X37] :
      ( ! [X26,X46] :
          ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X46)
         => ti(X3,X26) = ti(X3,X46) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_injI) ).

fof(fact_93_linorder__le__cases,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_linorder__le__cases) ).

fof(fact_115_leI,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_leI) ).

fof(fact_116_not__leE,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X34,X33] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_not__leE) ).

fof(fact_204_equalityD1,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_equalityD1) ).

fof(fact_203_equalityD2,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_equalityD2) ).

fof(tsy_c_FuncSet_OPi_res,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool))),pi(X3,X1)) = pi(X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_FuncSet_OPi_res) ).

fof(fact_223_linorder__neqE__nat,axiom,
    ! [X33,X34] :
      ( X33 != X34
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_linorder__neqE__nat) ).

fof(fact_164_add__right__cancel,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X15,X14,X17] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X14) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)
        <=> ti(X3,X15) = ti(X3,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_add__right__cancel) ).

fof(fact_161_add__right__imp__eq,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X22,X21,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X21) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)
         => ti(X3,X22) = ti(X3,X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_add__right__imp__eq) ).

fof(fact_162_add__imp__eq,axiom,
    ! [X3] :
      ( cancel146912293up_add(X3)
     => ! [X21,X22,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)
         => ti(X3,X22) = ti(X3,X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_add__imp__eq) ).

fof(fact_165_add__left__cancel,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X14,X15,X17] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X15) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)
        <=> ti(X3,X15) = ti(X3,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_add__left__cancel) ).

fof(fact_163_add__left__imp__eq,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X21,X22,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)
         => ti(X3,X22) = ti(X3,X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_add__left__imp__eq) ).

fof(fact_75_ext,axiom,
    ! [X3,X1,X37,X38] :
      ( ! [X26] : hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X38,X26)
     => ti(fun(X3,X1),X37) = ti(fun(X3,X1),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).

fof(fact_31_less__top,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X14] :
          ( ti(X3,X14) != top_top(X3)
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),top_top(X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_less__top) ).

fof(fact_132_top__le,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),top_top(X3)),X21))
         => ti(X3,X21) = top_top(X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_top__le) ).

fof(fact_131_top__unique,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),top_top(X3)),X14))
        <=> ti(X3,X14) = top_top(X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_top__unique) ).

fof(fact_352_not__one__le__zero,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),one_one(X3)),zero_zero(X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_not__one__le__zero) ).

fof(fact_354_not__one__less__zero,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),zero_zero(X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_not__one__less__zero) ).

fof(fact_30_not__top__less,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X21] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),top_top(X3)),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_not__top__less) ).

fof(fact_73_order__less__irrefl,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_order__less__irrefl) ).

fof(fact_324_not__less0,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_not__less0) ).

fof(fact_322_less__nat__zero__code,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_less__nat__zero__code) ).

fof(fact_318_less__zeroE,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_less__zeroE) ).

fof(fact_224_less__irrefl__nat,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_less__irrefl__nat) ).

fof(fact_221_less__not__refl,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_less__not__refl) ).

fof(help_fdisj_3_1_U,axiom,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87))
      | hBOOL(X86)
      | hBOOL(X87) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

fof(help_fconj_2_1_U,axiom,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87))
      | hBOOL(X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

fof(help_fconj_3_1_U,axiom,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87))
      | hBOOL(X87) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

fof(help_fequal_2_1_T,axiom,
    ! [X3,X33,X34] :
      ( ti(X3,X33) != ti(X3,X34)
      | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X33),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).

fof(help_If_1_1_T,axiom,
    ! [X3,X33,X34] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),hAPP(bool,fun(X3,fun(X3,X3)),if(X3),fTrue),X33),X34) = ti(X3,X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).

fof(help_If_2_1_T,axiom,
    ! [X3,X33,X34] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),hAPP(bool,fun(X3,fun(X3,X3)),if(X3),fFalse),X33),X34) = ti(X3,X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).

fof(tsy_c_Sum__Type_OPlus_res,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool))),sum_Plus(X3,X1)) = sum_Plus(X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Sum__Type_OPlus_res) ).

fof(fact_298_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,finite_card(X3),top_top(fun(X3,bool)))
       => ti(fun(X3,bool),X39) = top_top(fun(X3,bool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_card__eq__UNIV__imp__eq__UNIV) ).

fof(tsy_c_COMBS_res,axiom,
    ! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2))),combs(X3,X1,X2)) = combs(X3,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).

fof(fact_373_add__0__iff,axiom,
    ! [X3] :
      ( semiri456707255roduct(X3)
     => ! [X15,X14] :
          ( ti(X3,X15) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X14)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_add__0__iff) ).

fof(tsy_c_Product__Type_Oprod_Oprod__rec_res,axiom,
    ! [X1,X2,X3] : ti(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),product_prod_rec(X1,X2,X3)) = product_prod_rec(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Product__Type_Oprod_Oprod__rec_res) ).

fof(tsy_c_COMBC_res,axiom,
    ! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2))),combc(X3,X1,X2)) = combc(X3,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).

fof(tsy_c_COMBB_res,axiom,
    ! [X1,X2,X3] : ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).

fof(tsy_c_Hilbert__Choice_Oinv__into_res,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3))),hilbert_inv_into(X3,X1)) = hilbert_inv_into(X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hilbert__Choice_Oinv__into_res) ).

fof(tsy_c_FunDef_Oin__rel_res,axiom,
    ! [X3,X1] : ti(fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),in_rel(X3,X1)) = in_rel(X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_FunDef_Oin__rel_res) ).

fof(help_fconj_1_1_U,axiom,
    ! [X87,X86] :
      ( ~ hBOOL(X86)
      | ~ hBOOL(X87)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

fof(help_fdisj_1_1_U,axiom,
    ! [X87,X86] :
      ( ~ hBOOL(X86)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

fof(help_fdisj_2_1_U,axiom,
    ! [X86,X87] :
      ( ~ hBOOL(X87)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

fof(tsy_c_Set_Oimage_res,axiom,
    ! [X1,X3] : ti(fun(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool))),image(X1,X3)) = image(X1,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).

fof(fact_371_double__eq__0__iff,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14) = zero_zero(X3)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_double__eq__0__iff) ).

fof(fact_336_double__zero__sym,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( zero_zero(X3) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_double__zero__sym) ).

fof(fact_484_image__ident,axiom,
    ! [X3,X80] : hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),combi(X3)),X80) = ti(fun(X3,bool),X80),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_image__ident) ).

fof(tsy_c_hAPP_arg1,axiom,
    ! [X3,X2,X4,X5] : hAPP(X3,X2,ti(fun(X3,X2),X4),X5) = hAPP(X3,X2,X4,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).

fof(tsy_c_Fun_Oinj__on_res,axiom,
    ! [X3,X1] : ti(fun(fun(X3,X1),fun(fun(X3,bool),bool)),inj_on(X3,X1)) = inj_on(X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Fun_Oinj__on_res) ).

fof(help_COMBK_1_1_U,axiom,
    ! [X1,X3,X86,X87] : hAPP(X1,X3,hAPP(X3,fun(X1,X3),combk(X3,X1),X86),X87) = ti(X3,X86),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).

fof(fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_337_add__0,axiom,
    ! [X3] :
      ( comm_monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_add__0) ).

fof(fact_338_add__0__left,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_add__0__left) ).

fof(fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_334_add_Ocomm__neutral,axiom,
    ! [X3] :
      ( comm_monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_add_Ocomm__neutral) ).

fof(fact_335_add__0__right,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_add__0__right) ).

fof(tsy_c_Product__Type_OPair_res,axiom,
    ! [X3,X1] : ti(fun(X3,fun(X1,product_prod(X3,X1))),product_Pair(X3,X1)) = product_Pair(X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_res) ).

fof(help_ti_idem,axiom,
    ! [X84,X85] : ti(X84,ti(X84,X85)) = ti(X84,X85),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).

fof(tsy_c_hAPP_arg2,axiom,
    ! [X3,X2,X4,X5] : hAPP(X3,X2,X4,ti(X3,X5)) = hAPP(X3,X2,X4,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).

fof(tsy_c_hAPP_res,axiom,
    ! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).

fof(tsy_c_If_res,axiom,
    ! [X3] : ti(fun(bool,fun(X3,fun(X3,X3))),if(X3)) = if(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_If_res) ).

fof(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res,axiom,
    ! [X3] :
      ( linorder(X3)
     => ti(fun(X3,fun(X3,fun(X3,bool))),ord_atLeastLessThan(X3)) = ord_atLeastLessThan(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) ).

fof(tsy_c_member_res,axiom,
    ! [X3] : ti(fun(X3,fun(fun(X3,bool),bool)),member(X3)) = member(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).

fof(fact_356_card__infinite,axiom,
    ! [X3,X39] :
      ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_card__infinite) ).

fof(tsy_c_hBOOL_arg1,hypothesis,
    ! [X4] :
      ( hBOOL(ti(bool,X4))
    <=> hBOOL(X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).

fof(help_fNot_1_1_U,axiom,
    ! [X86] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X86))
      | ~ hBOOL(X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

fof(tsy_c_Set_OCollect_res,axiom,
    ! [X3] : ti(fun(fun(X3,bool),fun(X3,bool)),collect(X3)) = collect(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).

fof(fact_77_Collect__def,axiom,
    ! [X3,X11] : hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11) = ti(fun(X3,bool),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).

fof(tsy_c_COMBK_res,axiom,
    ! [X3,X1] : ti(fun(X3,fun(X1,X3)),combk(X3,X1)) = combk(X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_2_res,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_1_res,axiom,
    ! [X3] :
      ( ab_semigroup_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_0_res,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).

fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
    ! [X1] :
      ( ord(X1)
     => ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).

fof(tsy_c_Orderings_Oord__class_Oless_res,axiom,
    ! [X3] :
      ( ord(X3)
     => ti(fun(X3,fun(X3,bool)),ord_less(X3)) = ord_less(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_res) ).

fof(tsy_c_fequal_res,axiom,
    ! [X3] : ti(fun(X3,fun(X3,bool)),fequal(X3)) = fequal(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fequal_res) ).

fof(tsy_c_Finite__Set_Ocard_res,axiom,
    ! [X3] : ti(fun(fun(X3,bool),nat),finite_card(X3)) = finite_card(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).

fof(tsy_c_Finite__Set_Ofinite_res,axiom,
    ! [X1] : ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).

fof(help_fTrue_1_1_T,axiom,
    ! [X86] :
      ( ti(bool,X86) = fTrue
      | ti(bool,X86) = fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

fof(help_If_3_1_T,axiom,
    ! [X86] :
      ( ti(bool,X86) = fTrue
      | ti(bool,X86) = fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).

fof(tsy_c_COMBI_res,axiom,
    ! [X3] : ti(fun(X3,X3),combi(X3)) = combi(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).

fof(tsy_c_Int_Oring__1__class_OInts_res,axiom,
    ! [X3] :
      ( ring_1(X3)
     => ti(fun(X3,bool),ring_1_Ints(X3)) = ring_1_Ints(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Oring__1__class_OInts_res) ).

fof(tsy_c_Orderings_Otop__class_Otop_res,axiom,
    ! [X3] :
      ( top(X3)
     => ti(X3,top_top(X3)) = top_top(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Otop__class_Otop_res) ).

fof(tsy_c_Groups_Ozero__class_Ozero_res,axiom,
    ! [X3] :
      ( zero(X3)
     => ti(X3,zero_zero(X3)) = zero_zero(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_res) ).

fof(tsy_c_Groups_Oone__class_Oone_res,axiom,
    ! [X3] :
      ( one(X3)
     => ti(X3,one_one(X3)) = one_one(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).

fof(tsy_c_HOL_Oundefined_res,axiom,
    ! [X3] : ti(X3,undefined(X3)) = undefined(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).

fof(fact_81__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_33__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33__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(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).

fof(fact_91__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_,axiom,
    ? [X44] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
      & ! [X32] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X44))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X44),one_one(nat))))),lab)),lba)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_) ).

fof(fact_45_n_I2_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),n))
     => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_n_I2_J) ).

fof(fact_41_PiProf,axiom,
    ! [X29] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X29))),lab)),lba)),arrow_1111136790e_Prof)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_PiProf) ).

fof(fact_157_pred__subset__eq2,axiom,
    ! [X3,X1,X41,X40] :
      ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),hAPP(fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),combc(X3,fun(product_prod(X3,X1),bool),fun(X1,bool)),hAPP(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool)),X3),combc(X1,fun(product_prod(X3,X1),bool),bool)),hAPP(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool)))),combb(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),X3),hAPP(fun(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),combb(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),X1),member(product_prod(X3,X1)))),product_Pair(X3,X1)))),X41)),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),hAPP(fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),combc(X3,fun(product_prod(X3,X1),bool),fun(X1,bool)),hAPP(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool)),X3),combc(X1,fun(product_prod(X3,X1),bool),bool)),hAPP(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool)))),combb(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),X3),hAPP(fun(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),combb(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),X1),member(product_prod(X3,X1)))),product_Pair(X3,X1)))),X40)))
    <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(fun(product_prod(X3,X1),bool),fun(fun(product_prod(X3,X1),bool),bool),ord_less_eq(fun(product_prod(X3,X1),bool)),X41),X40)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_pred__subset__eq2) ).

fof(fact_433_card__less__Suc,axiom,
    ! [X42,X71] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_card__less__Suc) ).

fof(fact_184_xt4,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X15)),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X15))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X46),X26))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X46)),hAPP(X1,X3,X37,X26))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X17)),X14)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_xt4) ).

fof(fact_183_xt6,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & ord(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X15)),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X15))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),X26))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X46)),hAPP(X1,X3,X37,X26))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X17)),X14)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_xt6) ).

fof(fact_187_order__le__less__subst2,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X37,X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X15)),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X26),X46))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X37,X46))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X14)),X17)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_order__le__less__subst2) ).

fof(fact_216_order__less__le__subst2,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X37,X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X15)),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X26),X46))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X37,X46))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X14)),X17)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_order__less__le__subst2) ).

fof(fact_213_xt7,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X15)))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X46),X26))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X46)),hAPP(X3,X1,X37,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X14))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_xt7) ).

fof(fact_212_xt5,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X15),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),hAPP(X3,X1,X37,X15)))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),X26))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X46)),hAPP(X3,X1,X37,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X14))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_xt5) ).

fof(fact_186_order__less__le__subst1,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X17,X14,X37,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X15)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X46))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X26)),hAPP(X1,X3,X37,X46))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X17))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_order__less__le__subst1) ).

fof(fact_185_order__le__less__subst1,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X17,X14,X37,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),hAPP(X1,X3,X37,X15)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X46))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X26)),hAPP(X1,X3,X37,X46))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X17))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_order__le__less__subst1) ).

fof(fact_434_card__less,axiom,
    ! [X42,X71] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) != zero_zero(nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_card__less) ).

fof(fact_23_IIA__def,axiom,
    ! [X25] :
      ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X25))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => ! [X27] :
              ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X27),arrow_1111136790e_Prof))
             => ! [X19,X20] :
                  ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X27,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X27))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_IIA__def) ).

fof(fact_289_finite__Collect__disjI,axiom,
    ! [X3,X11,X50] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(bool,bool)),fun(fun(X3,bool),fun(X3,bool)),combs(X3,bool,bool),hAPP(fun(X3,bool),fun(X3,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3,bool),fun(X3,fun(bool,bool))),combb(bool,fun(bool,bool),X3),fdisj),X11)),X50))))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
        & hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X50))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_finite__Collect__disjI) ).

fof(fact_312_finite__M__bounded__by__nat,axiom,
    ! [X11,X42] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X11)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_finite__M__bounded__by__nat) ).

fof(fact_210_Pi__mono,axiom,
    ! [X1,X3,X43,X49,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X3,fun(X1,bool),X43,X26)),hAPP(X3,fun(X1,bool),X49,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(fun(X3,X1),bool),fun(fun(fun(X3,X1),bool),bool),ord_less_eq(fun(fun(X3,X1),bool)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X49))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Pi__mono) ).

fof(fact_272_Pi__cong,axiom,
    ! [X1,X3,X43,X37,X38,X39] :
      ( ! [X47] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X47),X39))
         => hAPP(X3,X1,X37,X47) = hAPP(X3,X1,X38,X47) )
     => ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
      <=> hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X38),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Pi__cong) ).

fof(fact_283_finite__Collect__conjI,axiom,
    ! [X3,X50,X11] :
      ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
        | hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X50))) )
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(bool,bool)),fun(fun(X3,bool),fun(X3,bool)),combs(X3,bool,bool),hAPP(fun(X3,bool),fun(X3,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3,bool),fun(X3,fun(bool,bool))),combb(bool,fun(bool,bool),X3),fconj),X11)),X50)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_finite__Collect__conjI) ).

fof(fact_315_finite__less__ub,axiom,
    ! [X66,X37] :
      ( ! [X44] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),hAPP(nat,nat,X37,X44)))
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X37)),X66)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_finite__less__ub) ).

fof(fact_273_Pi__I_H,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,fun(X1,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Pi__I_H) ).

fof(fact_147_Pi__I,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,fun(X1,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Pi__I) ).

fof(fact_457_Ints__odd__less__0,axiom,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),X14)),X14)),zero_zero(X3)))
          <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_Ints__odd__less__0) ).

fof(fact_303_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X1,X3,X43,X39,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X39))
         => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,hAPP(fun(X1,bool),X3,X25,X43)),hAPP(fun(X1,bool),X3,X25,X39)) = hAPP(fun(X1,bool),X3,X25,X39) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_folding__image__simple__idem_Osubset__idem) ).

fof(fact_270_funcsetI,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),X43)) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_funcsetI) ).

fof(fact_310_folding__image__simple__idem_Oin__idem,axiom,
    ! [X1,X3,X6,X39,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X39))
         => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,hAPP(X1,X3,X38,X6)),hAPP(fun(X1,bool),X3,X25,X39)) = hAPP(fun(X1,bool),X3,X25,X39) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_folding__image__simple__idem_Oin__idem) ).

fof(fact_278_card__bij,axiom,
    ! [X3,X1,X38,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
       => ( hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X38),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X43),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X39))))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X38),X43))
           => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
             => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
               => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X1,bool),nat,finite_card(X1),X43) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_card__bij) ).

fof(fact_24_unanimity__def,axiom,
    ! [X25] :
      ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X25))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => ! [X19,X20] :
              ( ! [X16] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X16)))
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_unanimity__def) ).

fof(fact_208_pred__subset__eq,axiom,
    ! [X3,X41,X40] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(X3,bool)),combc(X3,fun(X3,bool),bool),member(X3)),X41)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(X3,bool)),combc(X3,fun(X3,bool),bool),member(X3)),X40)))
    <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X41),X40)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_pred__subset__eq) ).

fof(fact_493_finite__range__imageI,axiom,
    ! [X2,X3,X1,X37,X38] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),top_top(fun(X1,bool)))))
     => hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X37),X38)),top_top(fun(X1,bool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_finite__range__imageI) ).

fof(fact_478_inv__into__into,axiom,
    ! [X3,X1,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),X39),X37),X6)),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_inv__into__into) ).

fof(fact_262_mono__nat__linear__lb,axiom,
    ! [X54,X57,X37] :
      ( ! [X32,X44] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X32),X44))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X37,X32)),hAPP(nat,nat,X37,X44))) )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X37,X54)),X57)),hAPP(nat,nat,X37,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_mono__nat__linear__lb) ).

fof(fact_443_lift__Suc__mono__less__iff,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X54,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X54)))
          <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_lift__Suc__mono__less__iff) ).

fof(fact_463_funcset__image,axiom,
    ! [X3,X1,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_funcset__image) ).

fof(fact_468_inj__image__subset__iff,axiom,
    ! [X3,X1,X39,X43,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43)))
      <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_inj__image__subset__iff) ).

fof(fact_441_lift__Suc__mono__le,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X72,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X72))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X72))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_lift__Suc__mono__le) ).

fof(fact_442_lift__Suc__mono__less,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X72,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X72))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X72))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_lift__Suc__mono__less) ).

fof(fact_494_subset__card__intvl__is__intvl,axiom,
    ! [X39,X57] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X39),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X57),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),hAPP(fun(nat,bool),nat,finite_card(nat),X39)))))
     => X39 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X57),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),hAPP(fun(nat,bool),nat,finite_card(nat),X39))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_subset__card__intvl__is__intvl) ).

fof(fact_274_card__inj,axiom,
    ! [X3,X1,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_card__inj) ).

fof(fact_140_funcset__mem,axiom,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_funcset__mem) ).

fof(fact_156_Pi__anti__mono,axiom,
    ! [X1,X3,X43,X48,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X48),X39))
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(fun(X3,X1),bool),fun(fun(fun(X3,X1),bool),bool),ord_less_eq(fun(fun(X3,X1),bool)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X48),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Pi__anti__mono) ).

fof(fact_462_atLeastLessThan__subset__iff,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15)),hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X14))
            | ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X17),X14))
              & hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X79)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_atLeastLessThan__subset__iff) ).

fof(fact_469_card__image__le,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))),hAPP(fun(X3,bool),nat,finite_card(X3),X39))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_card__image__le) ).

fof(fact_137_Pi__mem,axiom,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,fun(X1,bool),X43,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Pi__mem) ).

fof(fact_495_inj__on__strict__subset,axiom,
    ! [X3,X1,X39,X37,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_inj__on__strict__subset) ).

fof(fact_297_finite__Collect__not,axiom,
    ! [X3,X11] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(bool,bool),fun(fun(X3,bool),fun(X3,bool)),combb(bool,bool,X3),fNot),X11))))
      <=> hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_finite__Collect__not) ).

fof(fact_269_in__rel__def,axiom,
    ! [X1,X3,X41,X6,X7] :
      ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),in_rel(X3,X1),X41),X6),X7))
    <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X6),X7)),X41)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_in__rel__def) ).

fof(fact_279_finite__Collect__subsets,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hBOOL(hAPP(fun(fun(X3,bool),bool),bool,finite_finite_1(fun(X3,bool)),hAPP(fun(fun(X3,bool),bool),fun(fun(X3,bool),bool),collect(fun(X3,bool)),hAPP(fun(X3,bool),fun(fun(X3,bool),bool),hAPP(fun(fun(X3,bool),fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(fun(X3,bool),bool)),combc(fun(X3,bool),fun(X3,bool),bool),ord_less_eq(fun(X3,bool))),X39)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_finite__Collect__subsets) ).

fof(fact_89_inj__fun,axiom,
    ! [X2,X3,X1,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,fun(X2,X1)),fun(fun(X3,bool),bool),inj_on(X3,fun(X2,X1)),hAPP(fun(X3,X1),fun(X3,fun(X2,X1)),hAPP(fun(X1,fun(X2,X1)),fun(fun(X3,X1),fun(X3,fun(X2,X1))),combb(X1,fun(X2,X1),X3),combk(X1,X2)),X37)),top_top(fun(X3,bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_inj__fun) ).

fof(fact_48_mktop__Lin,axiom,
    ! [X6,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X8),X6)),arrow_2064824852le_Lin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_mktop__Lin) ).

fof(fact_49_mkbot__Lin,axiom,
    ! [X6,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X8),X6)),arrow_2064824852le_Lin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_mkbot__Lin) ).

fof(fact_174_add__le__cancel__right,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X17)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_add__le__cancel__right) ).

fof(fact_169_add__le__imp__le__right,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X21,X36,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_add__le__imp__le__right) ).

fof(fact_173_add__le__cancel__left,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X15)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_add__le__cancel__left) ).

fof(fact_168_add__le__imp__le__left,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_add__le__imp__le__left) ).

fof(fact_181_add__less__cancel__right,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X17)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_add__less__cancel__right) ).

fof(fact_176_add__less__imp__less__right,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X21,X36,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_add__less__imp__less__right) ).

fof(fact_180_add__less__cancel__left,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X15)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_add__less__cancel__left) ).

fof(fact_175_add__less__imp__less__left,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add__less__imp__less__left) ).

fof(fact_486_image__mono,axiom,
    ! [X1,X3,X37,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_image__mono) ).

fof(fact_257_nat__add__left__cancel__le,axiom,
    ! [X57,X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_nat__add__left__cancel__le) ).

fof(fact_242_nat__add__left__cancel__less,axiom,
    ! [X57,X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_nat__add__left__cancel__less) ).

fof(fact_182_le__funI,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( ! [X26] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X38,X26)))
         => hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_le__funI) ).

fof(fact_108_le__fun__def,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
        <=> ! [X26] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X38,X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_le__fun__def) ).

fof(conj_0,conjecture,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_51_const__Lin__Prof,axiom,
    ! [X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X8)),arrow_1111136790e_Prof)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_const__Lin__Prof) ).

fof(fact_276_inj__on__cong,axiom,
    ! [X1,X3,X37,X38,X39] :
      ( ! [X19] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X19),X39))
         => hAPP(X3,X1,X37,X19) = hAPP(X3,X1,X38,X19) )
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
      <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X38),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_inj__on__cong) ).

fof(fact_142_dictator__def,axiom,
    ! [X25,X42] :
      ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X25),X42))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_dictator__def) ).

fof(fact_170_add__mono,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_add__mono) ).

fof(fact_150_add__less__le__mono,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_add__less__le__mono) ).

fof(fact_151_add__le__less__mono,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_add__le__less__mono) ).

fof(fact_177_add__strict__mono,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_add__strict__mono) ).

fof(fact_263_less__mono__imp__le__mono,axiom,
    ! [X42,X63,X37] :
      ( ! [X16,X64] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X64))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X37,X16)),hAPP(nat,nat,X37,X64))) )
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X42),X63))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X37,X42)),hAPP(nat,nat,X37,X63))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_less__mono__imp__le__mono) ).

fof(fact_261_add__le__mono,axiom,
    ! [X52,X61,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X61))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_add__le__mono) ).

fof(fact_246_add__less__mono,axiom,
    ! [X52,X61,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X61))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__less__mono) ).

fof(fact_40__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

fof(fact_39__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(fact_344_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),zero_zero(X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_349_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_370_even__less__0__iff,axiom,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_even__less__0__iff) ).

fof(fact_476_Ints__add,axiom,
    ! [X3] :
      ( ring_1(X3)
     => ! [X15,X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),ring_1_Ints(X3)))
           => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X15)),ring_1_Ints(X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_Ints__add) ).

fof(fact_280_card__psubset,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43)))
         => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_card__psubset) ).

fof(fact_219_add__leD1,axiom,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_add__leD1) ).

fof(fact_220_add__leD2,axiom,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_add__leD2) ).

fof(fact_248_add__lessD1,axiom,
    ! [X58,X59,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X52))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X52)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_add__lessD1) ).

fof(fact_172_add__right__mono,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_add__right__mono) ).

fof(fact_171_add__left__mono,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_add__left__mono) ).

fof(fact_179_add__strict__right__mono,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__strict__right__mono) ).

fof(fact_178_add__strict__left__mono,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_add__strict__left__mono) ).

fof(fact_260_add__le__mono1,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X52))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_add__le__mono1) ).

fof(fact_245_add__less__mono1,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X52))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add__less__mono1) ).

fof(fact_464_finite__surj__inj,axiom,
    ! [X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39)))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_finite__surj__inj) ).

fof(fact_339_add__nonpos__nonpos,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_add__nonpos__nonpos) ).

fof(fact_358_add__neg__nonpos,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_add__neg__nonpos) ).

fof(fact_357_add__nonpos__neg,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_add__nonpos__neg) ).

fof(fact_346_add__neg__neg,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_add__neg__neg) ).

fof(fact_141_funcset__id,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(fun(X3,X3),bool),bool,hAPP(fun(X3,X3),fun(fun(fun(X3,X3),bool),bool),member(fun(X3,X3)),combi(X3)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X3,X3),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X3,bool)),fun(fun(X3,X3),bool)),pi(X3,X3),X39),hAPP(fun(X3,bool),fun(X3,fun(X3,bool)),combk(fun(X3,bool),X3),X39)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_funcset__id) ).

fof(fact_454_card_Oeq__fold__g,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,hAPP(nat,fun(fun(X3,bool),nat),hAPP(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat))),finite_fold_image(nat,X3),plus_plus(nat)),hAPP(nat,fun(X3,nat),combk(nat,X3),one_one(nat))),zero_zero(nat)),X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_card_Oeq__fold__g) ).

fof(fact_239_inj__on__add__nat,axiom,
    ! [X57,X60] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57)),X60)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_inj__on__add__nat) ).

fof(fact_285_finite__Collect__le__nat,axiom,
    ! [X57] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X57)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_finite__Collect__le__nat) ).

fof(fact_284_finite__Collect__less__nat,axiom,
    ! [X57] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X57)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_finite__Collect__less__nat) ).

fof(fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_481_imageI,axiom,
    ! [X1,X3,X37,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_imageI) ).

fof(fact_355_add__gr__0,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X54))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_add__gr__0) ).

fof(fact_306_finite__Plus__iff,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_finite__Plus__iff) ).

fof(fact_308_finite__PlusD_I1_J,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_finite__PlusD_I1_J) ).

fof(fact_309_finite__PlusD_I2_J,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_finite__PlusD_I2_J) ).

fof(fact_209_predicate2I,axiom,
    ! [X1,X3,X50,X11] :
      ( ! [X26,X46] :
          ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X26),X46))
         => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X26),X46)) )
     => hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_predicate2I) ).

fof(fact_343_add__nonneg__nonneg,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_add__nonneg__nonneg) ).

fof(fact_362_add__pos__nonneg,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_add__pos__nonneg) ).

fof(fact_361_add__nonneg__pos,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_add__nonneg__pos) ).

fof(fact_348_add__pos__pos,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_add__pos__pos) ).

fof(fact_490_range__composition,axiom,
    ! [X1,X3,X2,X37,X38] : hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X37),X38)),top_top(fun(X1,bool))) = hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X37),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),top_top(fun(X1,bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_range__composition) ).

fof(fact_341_add__increasing,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_add__increasing) ).

fof(fact_340_add__increasing2,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21,X36] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X36))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_add__increasing2) ).

fof(fact_360_add__strict__increasing,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_add__strict__increasing) ).

fof(fact_359_add__strict__increasing2,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_add__strict__increasing2) ).

fof(fact_347_pos__add__strict,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_pos__add__strict) ).

fof(fact_453_field__le__epsilon,axiom,
    ! [X3] :
      ( linordered_field(X3)
     => ! [X33,X34] :
          ( ! [X75] :
              ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X75))
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X34),X75))) )
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_field__le__epsilon) ).

fof(fact_483_image__image,axiom,
    ! [X1,X3,X2,X37,X38,X39] : hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X39)) = hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),combb(X1,X3,X2),X37),X38)),X39),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_image__image) ).

fof(fact_154_dense__le__bounded,axiom,
    ! [X3] :
      ( dense_linorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( ! [X47] :
                ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X47))
               => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X47),X34))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X47),X35)) ) )
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_dense__le__bounded) ).

fof(fact_15_split__paired__All,axiom,
    ! [X3,X1,X11] :
      ( ! [X18] : hBOOL(hAPP(product_prod(X3,X1),bool,X11,X18))
    <=> ! [X19,X20] : hBOOL(hAPP(product_prod(X3,X1),bool,X11,hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X19),X20))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_split__paired__All) ).

fof(fact_345_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_350_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_195_rev__predicate2D,axiom,
    ! [X1,X3,X50,X11,X6,X7] :
      ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X6),X7))
     => ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50))
       => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X6),X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_rev__predicate2D) ).

fof(fact_197_predicate2D,axiom,
    ! [X3,X1,X6,X7,X11,X50] :
      ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50))
     => ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X6),X7))
       => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X6),X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_predicate2D) ).

fof(fact_282_card__mono,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_card__mono) ).

fof(fact_281_psubset__card__mono,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_psubset__card__mono) ).

fof(fact_412_less__add__Suc1,axiom,
    ! [X58,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X51)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_less__add__Suc1) ).

fof(fact_411_less__add__Suc2,axiom,
    ! [X58,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X58)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_less__add__Suc2) ).

fof(fact_198_subset__trans,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X49)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_subset__trans) ).

fof(fact_193_psubset__subset__trans,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_psubset__subset__trans) ).

fof(fact_194_subset__psubset__trans,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_subset__psubset__trans) ).

fof(fact_215_psubset__trans,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_psubset__trans) ).

fof(fact_380_Suc__le__mono,axiom,
    ! [X29,X54] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X54)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X54)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_Suc__le__mono) ).

fof(fact_401_Suc__less__SucD,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),hAPP(nat,nat,suc,X53)))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_Suc__less__SucD) ).

fof(fact_393_Suc__less__eq,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_Suc__less__eq) ).

fof(fact_492_rangeI,axiom,
    ! [X3,X1,X37,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),hAPP(X1,X3,X37,X6)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_rangeI) ).

fof(fact_159_subset__inj__on,axiom,
    ! [X3,X1,X39,X37,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_subset__inj__on) ).

fof(fact_398_less__trans__Suc,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X59),X52))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X52)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_less__trans__Suc) ).

fof(fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_307_finite__Plus,axiom,
    ! [X1,X3,X43,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_finite__Plus) ).

fof(fact_200_set__rev__mp,axiom,
    ! [X3,X43,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_set__rev__mp) ).

fof(fact_202_in__mono,axiom,
    ! [X3,X6,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_in__mono) ).

fof(fact_199_set__mp,axiom,
    ! [X3,X6,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_set__mp) ).

fof(fact_189_subsetD,axiom,
    ! [X3,X17,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_subsetD) ).

fof(fact_214_psubsetD,axiom,
    ! [X3,X17,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_psubsetD) ).

fof(fact_104_le__funD,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X6,X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,X1,X38,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_le__funD) ).

fof(fact_94_le__funE,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X6,X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,X1,X38,X6))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_le__funE) ).

fof(fact_317_card__Plus__conv__if,axiom,
    ! [X1,X3,X43,X39] :
      ( ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
          & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) )
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) )
      & ( ~ ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
            & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) )
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = zero_zero(nat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_card__Plus__conv__if) ).

fof(fact_302_card__Plus,axiom,
    ! [X1,X3,X43,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_card__Plus) ).

fof(fact_470_eq__card__imp__inj__on,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)) = hAPP(fun(X3,bool),nat,finite_card(X3),X39)
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_eq__card__imp__inj__on) ).

fof(fact_471_inj__on__iff__eq__card,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
      <=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)) = hAPP(fun(X3,bool),nat,finite_card(X3),X39) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_inj__on__iff__eq__card) ).

fof(fact_264_termination__basic__simps_I3_J,axiom,
    ! [X35,X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_termination__basic__simps_I3_J) ).

fof(fact_258_trans__le__add1,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X51))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_trans__le__add1) ).

fof(fact_265_termination__basic__simps_I4_J,axiom,
    ! [X34,X33,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_termination__basic__simps_I4_J) ).

fof(fact_259_trans__le__add2,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X59))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_trans__le__add2) ).

fof(fact_267_termination__basic__simps_I1_J,axiom,
    ! [X35,X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_termination__basic__simps_I1_J) ).

fof(fact_243_trans__less__add1,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X51))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_trans__less__add1) ).

fof(fact_266_termination__basic__simps_I2_J,axiom,
    ! [X34,X33,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_termination__basic__simps_I2_J) ).

fof(fact_244_trans__less__add2,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X59))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_trans__less__add2) ).

fof(fact_448_Suc__lessE,axiom,
    ! [X58,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X52))
     => ~ ! [X64] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
           => X52 != hAPP(nat,nat,suc,X64) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_Suc__lessE) ).

fof(fact_383_Suc__leD,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_Suc__leD) ).

fof(fact_409_less__eq__Suc__le,axiom,
    ! [X29,X54] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),X54)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_less__eq__Suc__le) ).

fof(fact_407_Suc__le__eq,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_Suc__le__eq) ).

fof(fact_403_Suc__le__lessD,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Suc__le__lessD) ).

fof(fact_400_Suc__lessD,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_Suc__lessD) ).

fof(fact_375_Suc__mono,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),hAPP(nat,nat,suc,X53))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_Suc__mono) ).

fof(fact_97_order__trans,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_order__trans) ).

fof(fact_95_xt1_I6_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X33)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_xt1_I6_J) ).

fof(fact_126_order__less__le__trans,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_order__less__le__trans) ).

fof(fact_128_order__le__less__trans,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_order__le__less__trans) ).

fof(fact_55_order__less__trans,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_order__less__trans) ).

fof(fact_127_xt1_I7_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_xt1_I7_J) ).

fof(fact_129_xt1_I8_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_xt1_I8_J) ).

fof(fact_54_xt1_I10_J,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_xt1_I10_J) ).

fof(fact_236_le__trans,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X59),X52))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X52)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_le__trans) ).

fof(fact_247_less__add__eq__less,axiom,
    ! [X51,X53,X52,X61] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X61))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X61) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_less__add__eq__less) ).

fof(fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_166_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X3] :
      ( ab_semigroup_add(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),X45) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_404_le__less__Suc__eq,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54)))
      <=> X29 = X54 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_le__less__Suc__eq) ).

fof(fact_230_nat__add__assoc,axiom,
    ! [X51,X53,X52] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),X52) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X52)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_nat__add__assoc) ).

fof(fact_397_Suc__lessI,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => ( hAPP(nat,nat,suc,X51) != X53
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),X53)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_Suc__lessI) ).

fof(fact_405_Suc__leI,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_Suc__leI) ).

fof(fact_426_card__Collect__le__nat,axiom,
    ! [X29] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X29))) = hAPP(nat,nat,suc,X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_card__Collect__le__nat) ).

fof(fact_459_finite__imageI,axiom,
    ! [X1,X3,X76,X25] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X25))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X76),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_finite__imageI) ).

fof(fact_379_le__Suc__eq,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
        | X54 = hAPP(nat,nat,suc,X29) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_le__Suc__eq) ).

fof(fact_446_Suc__le__D,axiom,
    ! [X53,X73] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X53)),X73))
     => ? [X32] : X73 = hAPP(nat,nat,suc,X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_Suc__le__D) ).

fof(fact_438_inc__induct,axiom,
    ! [X11,X42,X63] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X42),X63))
     => ( hBOOL(hAPP(nat,bool,X11,X63))
       => ( ! [X16] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X63))
             => ( hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X16)))
               => hBOOL(hAPP(nat,bool,X11,X16)) ) )
         => hBOOL(hAPP(nat,bool,X11,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_inc__induct) ).

fof(fact_290_card__Collect__less__nat,axiom,
    ! [X29] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X29))) = X29,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_card__Collect__less__nat) ).

fof(fact_417_less__Suc__eq__0__disj,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( X54 = zero_zero(nat)
        | ? [X64] :
            ( X54 = hAPP(nat,nat,suc,X64)
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X64),X29)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_less__Suc__eq__0__disj) ).

fof(fact_211_subsetI,axiom,
    ! [X3,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X43)) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_subsetI) ).

fof(fact_466_finite__UNIV__inj__surj,axiom,
    ! [X3,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),top_top(fun(X3,bool))))
       => hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),top_top(fun(X3,bool))) = top_top(fun(X3,bool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_finite__UNIV__inj__surj) ).

fof(fact_392_less__Suc__eq,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | X54 = X29 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_less__Suc__eq) ).

fof(fact_408_less__Suc__eq__le,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_less__Suc__eq__le) ).

fof(fact_192_psubset__imp__subset,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_psubset__imp__subset) ).

fof(fact_313_finite__nat__set__iff__bounded__le,axiom,
    ! [X60] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
    <=> ? [X32] :
        ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_finite__nat__set__iff__bounded__le) ).

fof(fact_314_finite__nat__set__iff__bounded,axiom,
    ! [X60] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
    <=> ? [X32] :
        ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_finite__nat__set__iff__bounded) ).

fof(fact_467_finite__UNIV__surj__inj,axiom,
    ! [X3,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),top_top(fun(X3,bool))) = top_top(fun(X3,bool))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),top_top(fun(X3,bool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_finite__UNIV__surj__inj) ).

fof(fact_62_order__less__imp__triv,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X11,X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
           => hBOOL(X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_order__less__imp__triv) ).

fof(fact_381_le__SucI,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,suc,X53))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_le__SucI) ).

fof(fact_406_le__imp__less__Suc,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_le__imp__less__Suc) ).

fof(fact_396_less__SucI,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_less__SucI) ).

fof(fact_363_zero__less__two,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),one_one(X3)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_zero__less__two) ).

fof(fact_237_le__antisym,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X51))
       => X51 = X53 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_le__antisym) ).

fof(fact_149_less__add__one,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),one_one(X3)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_less__add__one) ).

fof(fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_153_dense__le,axiom,
    ! [X3] :
      ( dense_linorder(X3)
     => ! [X35,X34] :
          ( ! [X26] :
              ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X26),X34))
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X26),X35)) )
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_dense__le) ).

fof(fact_364_card__ge__0__finite,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X3,bool),nat,finite_card(X3),X39)))
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_card__ge__0__finite) ).

fof(fact_291_finite__subset,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_finite__subset) ).

fof(fact_292_rev__finite__subset,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_rev__finite__subset) ).

fof(fact_255_le__add1,axiom,
    ! [X53,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X51))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_le__add1) ).

fof(fact_254_le__add2,axiom,
    ! [X53,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_le__add2) ).

fof(fact_227_nat__less__cases,axiom,
    ! [X11,X54,X29] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
     => ( ( X54 = X29
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
       => ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
           => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_nat__less__cases) ).

fof(fact_229_nat__add__left__commute,axiom,
    ! [X33,X34,X35] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X33),X35)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_nat__add__left__commute) ).

fof(fact_201_predicate1D,axiom,
    ! [X3,X6,X11,X50] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X11),X50))
     => ( hBOOL(hAPP(X3,bool,X11,X6))
       => hBOOL(hAPP(X3,bool,X50,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_predicate1D) ).

fof(fact_205_rev__predicate1D,axiom,
    ! [X3,X50,X11,X6] :
      ( hBOOL(hAPP(X3,bool,X11,X6))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X11),X50))
       => hBOOL(hAPP(X3,bool,X50,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_rev__predicate1D) ).

fof(fact_410_less__iff__Suc__add,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> ? [X62] : X29 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_less__iff__Suc__add) ).

fof(help_COMBS_1_1_U,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2)),combs(X3,X1,X2),X86),X87),X88) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X86,X88),hAPP(X3,X1,X87,X88)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).

fof(fact_447_lessE,axiom,
    ! [X58,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X52))
     => ( X52 != hAPP(nat,nat,suc,X58)
       => ~ ! [X64] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
             => X52 != hAPP(nat,nat,suc,X64) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_lessE) ).

fof(fact_439_less__imp__Suc__add,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => ? [X62] : X53 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_less__imp__Suc__add) ).

fof(fact_121_order__less__imp__le,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_order__less__imp__le) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Odictator_res,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Odictator_res) ).

fof(fact_460_finite__atLeastLessThan,axiom,
    ! [X77,X66] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X77),X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_finite__atLeastLessThan) ).

fof(fact_369_less__imp__add__positive,axiom,
    ! [X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ? [X62] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X62))
          & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X62) = X59 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_less__imp__add__positive) ).

fof(fact_28_prod_Orecs,axiom,
    ! [X1,X2,X3,X28,X14,X15] : hAPP(product_prod(X1,X2),X3,hAPP(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3),product_prod_rec(X1,X2,X3),X28),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X14),X15)) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X28,X14),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_prod_Orecs) ).

fof(fact_252_le__neq__implies__less,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => ( X51 != X53
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_le__neq__implies__less) ).

fof(fact_250_le__eq__less__or__eq,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | X54 = X29 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_le__eq__less__or__eq) ).

fof(fact_249_nat__less__le,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
        & X54 != X29 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_nat__less__le) ).

fof(fact_268_termination__basic__simps_I5_J,axiom,
    ! [X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_termination__basic__simps_I5_J) ).

fof(fact_253_less__or__eq__imp__le,axiom,
    ! [X51,X53] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
        | X51 = X53 )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_less__or__eq__imp__le) ).

fof(fact_251_less__imp__le__nat,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_less__imp__le__nat) ).

fof(fact_416_less__Suc0,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,zero_zero(nat))))
    <=> X29 = zero_zero(nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_less__Suc0) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Ounanimity_res,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Ounanimity_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OIIA_res,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OIIA_res) ).

fof(fact_365_finite__UNIV__card__ge__0,axiom,
    ! [X3] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X3,bool),nat,finite_card(X3),top_top(fun(X3,bool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_finite__UNIV__card__ge__0) ).

fof(fact_271_linear__alt,axiom,
    ? [X65] : hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X65),arrow_2064824852le_Lin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_linear__alt) ).

fof(fact_452_nat__induct,axiom,
    ! [X29,X11] :
      ( hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( ! [X44] :
            ( hBOOL(hAPP(nat,bool,X11,X44))
           => hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X44))) )
       => hBOOL(hAPP(nat,bool,X11,X29)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_nat__induct) ).

fof(help_COMBB_1_1_U,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),combb(X1,X2,X3),X86),X87),X88) = hAPP(X1,X2,X86,hAPP(X3,X1,X87,X88)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

fof(help_COMBC_1_1_U,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(X1,fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2)),combc(X3,X1,X2),X86),X87),X88) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X86,X88),X87),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

fof(fact_389_add__Suc,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X51)),X53) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_add__Suc) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Obelow_res,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Obelow_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Oabove_res,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Oabove_res) ).

fof(fact_76_mem__def,axiom,
    ! [X3,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
    <=> hBOOL(hAPP(X3,bool,X39,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).

fof(fact_256_le__iff__add,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> ? [X62] : X29 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_le__iff__add) ).

fof(fact_107_linorder__linear,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_linorder__linear) ).

fof(fact_111_linorder__le__less__linear,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_linorder__le__less__linear) ).

fof(fact_316_bounded__nat__set__is__finite,axiom,
    ! [X29,X60] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X29)) )
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_bounded__nat__set__is__finite) ).

fof(fact_295_finite__Plus__UNIV__iff,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),top_top(fun(sum_sum(X3,X1),bool))))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_finite__Plus__UNIV__iff) ).

fof(fact_294_finite__Prod__UNIV,axiom,
    ! [X1,X3] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
       => hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,finite_finite_1(product_prod(X3,X1)),top_top(fun(product_prod(X3,X1),bool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_finite__Prod__UNIV) ).

fof(fact_222_nat__neq__iff,axiom,
    ! [X54,X29] :
      ( X54 != X29
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_nat__neq__iff) ).

fof(fact_234_nat__le__linear,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X51)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_nat__le__linear) ).

fof(fact_367_card_Oneutral,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( ( ? [X26] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => one_one(nat) = zero_zero(nat) )
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_card_Oneutral) ).

fof(fact_390_add__Suc__right,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,suc,X53)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_add__Suc__right) ).

fof(fact_388_add__Suc__shift,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X51)),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,suc,X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_add__Suc__shift) ).

fof(fact_372_finite__fun__UNIVD1,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,finite_finite_1(fun(X3,X1)),top_top(fun(fun(X3,X1),bool))))
     => ( hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool))) != hAPP(nat,nat,suc,zero_zero(nat))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_finite__fun__UNIVD1) ).

fof(fact_451_zero__induct,axiom,
    ! [X11,X57] :
      ( hBOOL(hAPP(nat,bool,X11,X57))
     => ( ! [X44] :
            ( hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X44)))
           => hBOOL(hAPP(nat,bool,X11,X44)) )
       => hBOOL(hAPP(nat,bool,X11,zero_zero(nat))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_zero__induct) ).

fof(fact_440_gr0__implies__Suc,axiom,
    ! [X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X53))
     => ? [X32] : X53 = hAPP(nat,nat,suc,X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_gr0__implies__Suc) ).

fof(fact_415_gr0__conv__Suc,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29))
    <=> ? [X32] : X29 = hAPP(nat,nat,suc,X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_gr0__conv__Suc) ).

fof(fact_461__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123,axiom,
    ~ ! [X78] :
        ( hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),X78),top_top(fun(arrow_660593299e_indi,bool))))
       => hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),X78),top_top(fun(arrow_660593299e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123) ).

fof(fact_88_Pi__UNIV,axiom,
    ! [X3,X1,X39] : hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),top_top(fun(X1,bool)))) = top_top(fun(fun(X3,X1),bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Pi__UNIV) ).

fof(fact_376_zero__less__Suc,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X53))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_zero__less__Suc) ).

fof(fact_374_lessI,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,suc,X53))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_lessI) ).

fof(fact_323_neq0__conv,axiom,
    ! [X29] :
      ( X29 != zero_zero(nat)
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_neq0__conv) ).

fof(fact_329_le__0__eq,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),zero_zero(nat)))
    <=> X29 = zero_zero(nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_le__0__eq) ).

fof(fact_321_gr__implies__not0,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => X53 != zero_zero(nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_gr__implies__not0) ).

fof(fact_226_less__not__refl3,axiom,
    ! [X55,X56] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
     => X55 != X56 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_less__not__refl3) ).

fof(fact_225_less__not__refl2,axiom,
    ! [X53,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X51))
     => X51 != X53 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_less__not__refl2) ).

fof(fact_232_nat__add__right__cancel,axiom,
    ! [X54,X57,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)
    <=> X54 = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_nat__add__right__cancel) ).

fof(fact_231_nat__add__left__cancel,axiom,
    ! [X57,X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)
    <=> X54 = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_nat__add__left__cancel) ).

fof(fact_299_finite__fun__UNIVD2,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,finite_finite_1(fun(X3,X1)),top_top(fun(fun(X3,X1),bool))))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_finite__fun__UNIVD2) ).

fof(fact_158_subset__UNIV,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),top_top(fun(X3,bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_subset__UNIV) ).

fof(fact_414_add__is__1,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
          & X29 = zero_zero(nat) )
        | ( X54 = zero_zero(nat)
          & X29 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_add__is__1) ).

fof(fact_413_one__is__add,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29)
    <=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
          & X29 = zero_zero(nat) )
        | ( X54 = zero_zero(nat)
          & X29 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_one__is__add) ).

fof(fact_207_subset__refl,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X39)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_subset__refl) ).

fof(tsy_v_F_res,hypothesis,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_F_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omktop_res,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omktop_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omkbot_res,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omkbot_res) ).

fof(fact_139_inj__on__id2,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),combi(X3)),X39)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_inj__on__id2) ).

fof(fact_27_iso__tuple__UNIV__I,axiom,
    ! [X3,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),top_top(fun(X3,bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_iso__tuple__UNIV__I) ).

fof(fact_26_UNIV__I,axiom,
    ! [X3,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),top_top(fun(X3,bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_UNIV__I) ).

fof(fact_418_inj__Suc,axiom,
    ! [X60] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X60)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_inj__Suc) ).

fof(fact_474_Ints__0,axiom,
    ! [X3] :
      ( ring_1(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),zero_zero(X3)),ring_1_Ints(X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_Ints__0) ).

fof(fact_475_Ints__1,axiom,
    ! [X3] :
      ( ring_1(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),one_one(X3)),ring_1_Ints(X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_Ints__1) ).

fof(fact_296_finite__option__UNIV,axiom,
    ! [X3] :
      ( hBOOL(hAPP(fun(option(X3),bool),bool,finite_finite_1(option(X3)),top_top(fun(option(X3),bool))))
    <=> hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_finite__option__UNIV) ).

fof(fact_351_zero__le__one,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),one_one(X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_zero__le__one) ).

fof(fact_353_zero__less__one,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),one_one(X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_zero__less__one) ).

fof(fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_130_top__greatest,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),top_top(X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_top__greatest) ).

fof(fact_311_UNIV__Plus__UNIV,axiom,
    ! [X1,X3] : hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),top_top(fun(X3,bool))),top_top(fun(X1,bool))) = top_top(fun(sum_sum(X3,X1),bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_UNIV__Plus__UNIV) ).

fof(fact_105_order__eq__refl,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( X33 = X34
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order__eq__refl) ).

fof(fact_90_order__refl,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_order__refl) ).

fof(fact_320_gr0I,axiom,
    ! [X53] :
      ( X53 != zero_zero(nat)
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_gr0I) ).

fof(fact_330_less__eq__nat_Osimps_I1_J,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_less__eq__nat_Osimps_I1_J) ).

fof(fact_319_le0,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_le0) ).

fof(fact_235_eq__imp__le,axiom,
    ! [X51,X53] :
      ( X51 = X53
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_eq__imp__le) ).

fof(fact_233_le__refl,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X53)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_le__refl) ).

fof(fact_228_nat__add__commute,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X51),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_nat__add__commute) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OProf_res,axiom,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OProf_res) ).

fof(fact_327_add__is__0,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29) = zero_zero(nat)
    <=> ( X54 = zero_zero(nat)
        & X29 = zero_zero(nat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_add__is__0) ).

fof(fact_328_add__eq__self__zero,axiom,
    ! [X51,X53] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53) = X51
     => X53 = zero_zero(nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_add__eq__self__zero) ).

fof(fact_444_Suc__eq__plus1__left,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X53),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_Suc__eq__plus1__left) ).

fof(fact_445_Suc__eq__plus1,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),one_one(nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_Suc__eq__plus1) ).

fof(fact_425_less__eq__Suc__le__raw,axiom,
    ! [X26] : hAPP(nat,fun(nat,bool),ord_less(nat),X26) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_less__eq__Suc__le__raw) ).

fof(fact_304_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_infinite__UNIV__nat) ).

fof(fact_74_UNIV__def,axiom,
    ! [X3] : top_top(fun(X3,bool)) = hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(bool,fun(X3,bool),combk(bool,X3),fTrue)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_UNIV__def) ).

fof(tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OLin_res,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OLin_res) ).

fof(tsy_v_P_____res,hypothesis,
    ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_P_____res) ).

fof(fact_325_plus__nat_Oadd__0,axiom,
    ! [X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X53) = X53,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_plus__nat_Oadd__0) ).

fof(fact_326_Nat_Oadd__0__right,axiom,
    ! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),zero_zero(nat)) = X51,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Nat_Oadd__0__right) ).

fof(fact_385_nat_Oinject,axiom,
    ! [X67,X68] :
      ( hAPP(nat,nat,suc,X67) = hAPP(nat,nat,suc,X68)
    <=> X67 = X68 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_nat_Oinject) ).

fof(fact_384_Suc__inject,axiom,
    ! [X33,X34] :
      ( hAPP(nat,nat,suc,X33) = hAPP(nat,nat,suc,X34)
     => X33 = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_Suc__inject) ).

fof(fact_293_finite__UNIV,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_finite__UNIV) ).

fof(fact_25_top1I,axiom,
    ! [X3,X6] : hBOOL(hAPP(X3,bool,top_top(fun(X3,bool)),X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_top1I) ).

fof(fact_287_finite__code,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => ! [X39] : hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_finite__code) ).

fof(fact_286_finite,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => ! [X39] : hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_finite) ).

fof(tsy_v_Lba_____res,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_Lba_____res) ).

fof(tsy_v_Lab_____res,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_Lab_____res) ).

fof(tsy_c_fdisj_res,axiom,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).

fof(tsy_c_fconj_res,axiom,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fconj_res) ).

fof(help_fNot_2_1_U,axiom,
    ! [X86] :
      ( hBOOL(X86)
      | hBOOL(hAPP(bool,bool,fNot,X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

fof(fact_422_Suc__not__Zero,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) != zero_zero(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_Suc__not__Zero) ).

fof(fact_421_nat_Osimps_I3_J,axiom,
    ! [X69] : hAPP(nat,nat,suc,X69) != zero_zero(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_nat_Osimps_I3_J) ).

fof(fact_419_Suc__neq__Zero,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) != zero_zero(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_Suc__neq__Zero) ).

fof(fact_424_Zero__not__Suc,axiom,
    ! [X51] : zero_zero(nat) != hAPP(nat,nat,suc,X51),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_Zero__not__Suc) ).

fof(fact_423_nat_Osimps_I2_J,axiom,
    ! [X70] : zero_zero(nat) != hAPP(nat,nat,suc,X70),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_nat_Osimps_I2_J) ).

fof(fact_420_Zero__neq__Suc,axiom,
    ! [X51] : zero_zero(nat) != hAPP(nat,nat,suc,X51),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_Zero__neq__Suc) ).

fof(fact_386_Suc__n__not__n,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) != X53,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_Suc__n__not__n) ).

fof(fact_387_n__not__Suc__n,axiom,
    ! [X53] : X53 != hAPP(nat,nat,suc,X53),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_n__not__Suc__n) ).

fof(tsy_c_Nat_OSuc_res,axiom,
    ti(fun(nat,nat),suc) = suc,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_OSuc_res) ).

fof(tsy_c_fNot_res,axiom,
    ti(fun(bool,bool),fNot) = fNot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fNot_res) ).

fof(tsy_v_h_____res,axiom,
    ti(fun(arrow_660593299e_indi,nat),h) = h,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_h_____res) ).

fof(fact_29_top__apply,axiom,
    ! [X1,X3] :
      ( top(X3)
     => ! [X6] : hAPP(X1,X3,top_top(fun(X1,X3)),X6) = top_top(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_top__apply) ).

fof(fact_450_nat_Oexhaust,axiom,
    ! [X34] :
      ( X34 != zero_zero(nat)
     => ~ ! [X74] : X34 != hAPP(nat,nat,suc,X74) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_nat_Oexhaust) ).

fof(fact_449_not0__implies__Suc,axiom,
    ! [X53] :
      ( X53 != zero_zero(nat)
     => ? [X32] : X53 = hAPP(nat,nat,suc,X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_not0__implies__Suc) ).

fof(tsy_v_n_____res,axiom,
    ti(nat,n) = n,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_n_____res) ).

fof(tsy_c_fTrue_res,axiom,
    ti(bool,fTrue) = fTrue,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).

fof(tsy_c_fFalse_res,axiom,
    ti(bool,fFalse) = fFalse,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).

fof(tsy_v_e_____res,axiom,
    ti(arrow_490897120le_alt,e) = e,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_e_____res) ).

fof(tsy_v_d_____res,hypothesis,
    ti(arrow_490897120le_alt,d) = d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_d_____res) ).

fof(tsy_v_c_____res,hypothesis,
    ti(arrow_490897120le_alt,c) = c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_c_____res) ).

fof(tsy_v_b_____res,axiom,
    ti(arrow_490897120le_alt,b) = b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_b_____res) ).

fof(tsy_v_a_____res,axiom,
    ti(arrow_490897120le_alt,a) = a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_a_____res) ).

fof(arity_sum___Finite__Set_Ofinite,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(sum_sum(X82,X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).

fof(arity_fun___Finite__Set_Ofinite,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(fun(X82,X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).

fof(arity_prod___Finite__Set_Ofinite,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(product_prod(X82,X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).

fof(arity_fun___Orderings_Oorder,axiom,
    ! [X82,X83] :
      ( order(X83)
     => order(fun(X82,X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).

fof(arity_fun___Orderings_Opreorder,axiom,
    ! [X82,X83] :
      ( preorder(X83)
     => preorder(fun(X82,X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).

fof(arity_fun___Orderings_Otop,axiom,
    ! [X82,X83] :
      ( top(X83)
     => top(fun(X82,X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).

fof(arity_fun___Orderings_Oord,axiom,
    ! [X82,X83] :
      ( ord(X83)
     => ord(fun(X82,X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).

fof(fact_333_one__neq__zero,axiom,
    ! [X3] :
      ( zero_neq_one(X3)
     => one_one(X3) != zero_zero(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_one__neq__zero) ).

fof(fact_332_zero__neq__one,axiom,
    ! [X3] :
      ( zero_neq_one(X3)
     => zero_zero(X3) != one_one(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_zero__neq__one) ).

fof(arity_Option_Ooption___Finite__Set_Ofinite,axiom,
    ! [X83] :
      ( finite_finite(X83)
     => finite_finite(option(X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option_Ooption___Finite__Set_Ofinite) ).

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(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    file('/export/starexec/sandbox2/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(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    file('/export/starexec/sandbox2/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(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    file('/export/starexec/sandbox2/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(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)),
    file('/export/starexec/sandbox2/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_80_n_I3_J,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_n_I3_J) ).

fof(fact_32_assms_I1_J,axiom,
    hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_assms_I1_J) ).

fof(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))),
    file('/export/starexec/sandbox2/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_38__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

fof(fact_37__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

fof(fact_3__096P_A_058_AProf_096,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

fof(fact_138_Prof__def,axiom,
    arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Prof__def) ).

fof(fact_35__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35__096Lba_A_058_ALin_096) ).

fof(fact_34__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34__096Lab_A_058_ALin_096) ).

fof(fact_19_n_I1_J,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n_I1_J) ).

fof(fact_456_surjh,axiom,
    hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_surjh) ).

fof(fact_20_injh,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_injh) ).

fof(fact_1_u,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_u) ).

fof(fact_0_assms_I3_J,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).

fof(fact_277_finite__indi,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_finite__indi) ).

fof(fact_288_card__UNIV__unit,axiom,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_card__UNIV__unit) ).

fof(fact_402_One__nat__def,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_One__nat__def) ).

fof(arity_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
    comm_semiring_1(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).

fof(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc,axiom,
    semiri456707255roduct(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).

fof(arity_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
    ordere216010020id_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).

fof(arity_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
    comm_monoid_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).

fof(arity_Nat_Onat___Rings_Ozero__neq__one,axiom,
    zero_neq_one(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).

fof(arity_Product__Type_Ounit___Finite__Set_Ofinite,axiom,
    finite_finite(product_unit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product__Type_Ounit___Finite__Set_Ofinite) ).

fof(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
    finite_finite(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).

fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
    ordere779506340up_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    ordere236663937imp_le(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
    cancel146912293up_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
    ordere223160158up_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat_Onat___Rings_Olinordered__semidom,axiom,
    linordered_semidom(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).

fof(arity_Nat_Onat___Orderings_Oorder,axiom,
    order(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).

fof(arity_HOL_Obool___Orderings_Oorder,axiom,
    order(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).

fof(arity_Nat_Onat___Orderings_Opreorder,axiom,
    preorder(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).

fof(arity_HOL_Obool___Orderings_Opreorder,axiom,
    preorder(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).

fof(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

fof(arity_Nat_Onat___Orderings_Olinorder,axiom,
    linorder(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).

fof(arity_HOL_Obool___Orderings_Otop,axiom,
    top(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).

fof(arity_Nat_Onat___Orderings_Oord,axiom,
    ord(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).

fof(arity_HOL_Obool___Orderings_Oord,axiom,
    ord(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).

fof(arity_Nat_Onat___Groups_Ozero,axiom,
    zero(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

fof(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
    cancel_semigroup_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Oab__semigroup__add,axiom,
    ab_semigroup_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Omonoid__add,axiom,
    monoid_add(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).

fof(arity_Nat_Onat___Groups_Oone,axiom,
    one(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).

fof(fact_2__096c_A_126_061_Ad_096,axiom,
    c != d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).

fof(fact_36__096a_A_126_061_Ab_096,axiom,
    a != b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36__096a_A_126_061_Ab_096) ).

fof(i_0_608,plain,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_44__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_609,plain,
    ! [X6,X7,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
       => ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8))
        <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X7),X6)),X8)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_46_notin__Lin__iff]) ).

fof(i_0_610,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_122_linorder__antisym__conv2]) ).

fof(i_0_611,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X7,X6] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_69_linorder__antisym__conv3]) ).

fof(i_0_612,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_117_linorder__antisym__conv1]) ).

fof(i_0_613,plain,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X33,X34] :
          ( ti(X3,X33) != ti(X3,X34)
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_160_linorder__neqE__linordered__idom]) ).

fof(i_0_614,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
            | ti(X3,X6) = ti(X3,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_71_not__less__iff__gr__or__eq]) ).

fof(i_0_615,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ti(X3,X33) != ti(X3,X34)
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_68_linorder__neqE]) ).

fof(i_0_616,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( ti(X3,X33) != ti(X3,X34)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_52_linorder__cases]) ).

fof(i_0_617,plain,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => ~ ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
         => ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ) ),
    inference(fof_simplification,[status(thm)],[fact_196_equalityE]) ).

fof(i_0_618,plain,
    ! [X3,X33,X34] :
      ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X33),X34))
      | ti(X3,X33) = ti(X3,X34) ),
    inference(fof_simplification,[status(thm)],[help_fequal_1_1_T]) ).

fof(i_0_619,plain,
    ~ ! [X44] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
       => ( ! [X32] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X44))
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) )
         => ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X44),one_one(nat))))),lab)),lba)))) ) ),
    inference(fof_simplification,[status(thm)],[fact_92__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O]) ).

fof(i_0_620,plain,
    ! [X42,X71] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) ),
    inference(fof_simplification,[status(thm)],[fact_435_card__less__Suc2]) ).

fof(i_0_621,plain,
    ! [X1798,X1799,X1800,X1801,X1802,X1803] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1802),X1803)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1799)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1800),X1801)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1798)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1802),X1803)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1799,esk1_6(X1798,X1799,X1800,X1801,X1802,X1803))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1800),X1801)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1798,esk1_6(X1798,X1799,X1800,X1801,X1802,X1803))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1798),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1799),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1803) = ti(arrow_490897120le_alt,X1800)
        | ti(arrow_490897120le_alt,X1802) = ti(arrow_490897120le_alt,X1801)
        | ti(arrow_490897120le_alt,X1800) = ti(arrow_490897120le_alt,X1801)
        | ti(arrow_490897120le_alt,X1802) = ti(arrow_490897120le_alt,X1803) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1800),X1801)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1798)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1802),X1803)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1799)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1802),X1803)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1799,esk1_6(X1798,X1799,X1800,X1801,X1802,X1803))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1800),X1801)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1798,esk1_6(X1798,X1799,X1800,X1801,X1802,X1803))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1798),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1799),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1803) = ti(arrow_490897120le_alt,X1800)
        | ti(arrow_490897120le_alt,X1802) = ti(arrow_490897120le_alt,X1801)
        | ti(arrow_490897120le_alt,X1800) = ti(arrow_490897120le_alt,X1801)
        | ti(arrow_490897120le_alt,X1802) = ti(arrow_490897120le_alt,X1803) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1802),X1803)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1799)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1800),X1801)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1798)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1802),X1803)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1799,esk1_6(X1798,X1799,X1800,X1801,X1802,X1803))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1800),X1801)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1798,esk1_6(X1798,X1799,X1800,X1801,X1802,X1803))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1798),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1799),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1803) = ti(arrow_490897120le_alt,X1800)
        | ti(arrow_490897120le_alt,X1802) = ti(arrow_490897120le_alt,X1801)
        | ti(arrow_490897120le_alt,X1800) = ti(arrow_490897120le_alt,X1801)
        | ti(arrow_490897120le_alt,X1802) = ti(arrow_490897120le_alt,X1803) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1800),X1801)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1798)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1802),X1803)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1799)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1802),X1803)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1799,esk1_6(X1798,X1799,X1800,X1801,X1802,X1803))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1800),X1801)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1798,esk1_6(X1798,X1799,X1800,X1801,X1802,X1803))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1798),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1799),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1803) = ti(arrow_490897120le_alt,X1800)
        | ti(arrow_490897120le_alt,X1802) = ti(arrow_490897120le_alt,X1801)
        | ti(arrow_490897120le_alt,X1800) = ti(arrow_490897120le_alt,X1801)
        | ti(arrow_490897120le_alt,X1802) = ti(arrow_490897120le_alt,X1803) ) ),
    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_622,plain,
    ! [X3403,X3404] : hAPP(X3403,X3403,combi(X3403),X3404) = ti(X3403,X3404),
    inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).

fof(i_0_623,plain,
    ! [X1805,X1806,X1807,X1808,X1809,X1810] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1809),X1810)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1806,esk2_6(X1805,X1806,X1807,X1808,X1809,X1810))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1807),X1808)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1805,esk2_6(X1805,X1806,X1807,X1808,X1809,X1810))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1809),X1810)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1806)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1807),X1808)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1805)))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1805),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1806),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1810) = ti(arrow_490897120le_alt,X1807)
        | ti(arrow_490897120le_alt,X1809) = ti(arrow_490897120le_alt,X1808)
        | ti(arrow_490897120le_alt,X1807) = ti(arrow_490897120le_alt,X1808)
        | ti(arrow_490897120le_alt,X1809) = ti(arrow_490897120le_alt,X1810) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1809),X1810)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1806,esk2_6(X1805,X1806,X1807,X1808,X1809,X1810))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1807),X1808)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1805,esk2_6(X1805,X1806,X1807,X1808,X1809,X1810))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1809),X1810)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1806)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1807),X1808)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1805)))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1805),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1806),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1810) = ti(arrow_490897120le_alt,X1807)
        | ti(arrow_490897120le_alt,X1809) = ti(arrow_490897120le_alt,X1808)
        | ti(arrow_490897120le_alt,X1807) = ti(arrow_490897120le_alt,X1808)
        | ti(arrow_490897120le_alt,X1809) = ti(arrow_490897120le_alt,X1810) ) ),
    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_624,plain,
    ! [X1818,X1819,X1820,X1821,X1822,X1823] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1822),X1823)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1819)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1820),X1821)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1818)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1822),X1823)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1819,esk4_6(X1818,X1819,X1820,X1821,X1822,X1823))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1820),X1821)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1818,esk4_6(X1818,X1819,X1820,X1821,X1822,X1823))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1818),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1819),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1820) = ti(arrow_490897120le_alt,X1821)
        | ti(arrow_490897120le_alt,X1822) = ti(arrow_490897120le_alt,X1823) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1820),X1821)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1818)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1822),X1823)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1819)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1822),X1823)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1819,esk4_6(X1818,X1819,X1820,X1821,X1822,X1823))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1820),X1821)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1818,esk4_6(X1818,X1819,X1820,X1821,X1822,X1823))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1818),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1819),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1820) = ti(arrow_490897120le_alt,X1821)
        | ti(arrow_490897120le_alt,X1822) = ti(arrow_490897120le_alt,X1823) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1822),X1823)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1819)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1820),X1821)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1818)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1822),X1823)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1819,esk4_6(X1818,X1819,X1820,X1821,X1822,X1823))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1820),X1821)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1818,esk4_6(X1818,X1819,X1820,X1821,X1822,X1823))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1818),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1819),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1820) = ti(arrow_490897120le_alt,X1821)
        | ti(arrow_490897120le_alt,X1822) = ti(arrow_490897120le_alt,X1823) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1820),X1821)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1818)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1822),X1823)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1819)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1822),X1823)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1819,esk4_6(X1818,X1819,X1820,X1821,X1822,X1823))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1820),X1821)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1818,esk4_6(X1818,X1819,X1820,X1821,X1822,X1823))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1818),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1819),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1820) = ti(arrow_490897120le_alt,X1821)
        | ti(arrow_490897120le_alt,X1822) = ti(arrow_490897120le_alt,X1823) ) ),
    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_625,plain,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_82__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_626,plain,
    ! [X16] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)))
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),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_627,plain,
    ! [X1812,X1813,X1814,X1815,X1816] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1815),X1816)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1813)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1816),X1814)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1812)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1815),X1816)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1813,esk3_5(X1812,X1813,X1814,X1815,X1816))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1816),X1814)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1812,esk3_5(X1812,X1813,X1814,X1815,X1816))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1812),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1813),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1815) = ti(arrow_490897120le_alt,X1814)
        | ti(arrow_490897120le_alt,X1816) = ti(arrow_490897120le_alt,X1814)
        | ti(arrow_490897120le_alt,X1815) = ti(arrow_490897120le_alt,X1816) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1816),X1814)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1812)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1815),X1816)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1813)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1815),X1816)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1813,esk3_5(X1812,X1813,X1814,X1815,X1816))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1816),X1814)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1812,esk3_5(X1812,X1813,X1814,X1815,X1816))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1812),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1813),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1815) = ti(arrow_490897120le_alt,X1814)
        | ti(arrow_490897120le_alt,X1816) = ti(arrow_490897120le_alt,X1814)
        | ti(arrow_490897120le_alt,X1815) = ti(arrow_490897120le_alt,X1816) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1815),X1816)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1813)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1816),X1814)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1812)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1815),X1816)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1813,esk3_5(X1812,X1813,X1814,X1815,X1816))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1816),X1814)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1812,esk3_5(X1812,X1813,X1814,X1815,X1816))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1812),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1813),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1815) = ti(arrow_490897120le_alt,X1814)
        | ti(arrow_490897120le_alt,X1816) = ti(arrow_490897120le_alt,X1814)
        | ti(arrow_490897120le_alt,X1815) = ti(arrow_490897120le_alt,X1816) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1816),X1814)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1812)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1815),X1816)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1813)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1815),X1816)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1813,esk3_5(X1812,X1813,X1814,X1815,X1816))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1816),X1814)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1812,esk3_5(X1812,X1813,X1814,X1815,X1816))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1812),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1813),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1815) = ti(arrow_490897120le_alt,X1814)
        | ti(arrow_490897120le_alt,X1816) = ti(arrow_490897120le_alt,X1814)
        | ti(arrow_490897120le_alt,X1815) = ti(arrow_490897120le_alt,X1816) ) ),
    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_628,plain,
    ! [X2028,X2029] :
      ( ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk23_2(X2028,X2029)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2029),X2028))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2029),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) )
      & ( ti(arrow_490897120le_alt,esk24_2(X2028,X2029)) != ti(arrow_490897120le_alt,esk25_2(X2028,X2029))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2029),X2028))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2029),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X2028,X2029)),esk25_2(X2028,X2029))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk23_2(X2028,X2029),X2028)))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2029),X2028))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2029),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X2028,X2029)),esk25_2(X2028,X2029))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2029,esk23_2(X2028,X2029))))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2029),X2028))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2029),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_dictatorI])])])]) ).

fof(i_0_629,plain,
    ! [X1900] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1900) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1900) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1900)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1900)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_608])])]) ).

fof(i_0_630,plain,
    ! [X1825,X1826,X1827,X1828] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1827),X1828)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1826)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1828),X1827)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1825)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1827),X1828)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1826,esk5_4(X1825,X1826,X1827,X1828))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1828),X1827)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1825,esk5_4(X1825,X1826,X1827,X1828))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1825),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1826),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1827) = ti(arrow_490897120le_alt,X1828) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1828),X1827)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1825)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1827),X1828)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1826)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1827),X1828)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1826,esk5_4(X1825,X1826,X1827,X1828))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1828),X1827)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1825,esk5_4(X1825,X1826,X1827,X1828))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1825),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1826),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1827) = ti(arrow_490897120le_alt,X1828) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1827),X1828)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1826)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1828),X1827)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1825)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1827),X1828)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1826,esk5_4(X1825,X1826,X1827,X1828))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1828),X1827)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1825,esk5_4(X1825,X1826,X1827,X1828))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1825),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1826),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1827) = ti(arrow_490897120le_alt,X1828) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1828),X1827)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1825)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1827),X1828)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X1826)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1827),X1828)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1826,esk5_4(X1825,X1826,X1827,X1828))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1828),X1827)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1825,esk5_4(X1825,X1826,X1827,X1828))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1825),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1826),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X1827) = ti(arrow_490897120le_alt,X1828) ) ),
    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_631,plain,
    ! [X2578,X2579,X2580,X2581,X2582] :
      ( ( ti(arrow_490897120le_alt,X2578) != ti(arrow_490897120le_alt,X2579)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2579) != ti(arrow_490897120le_alt,X2581)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2582)),X2580))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2578) != ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2582)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2582),X2579)),X2580))
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2581)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),X2580))
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2579) != ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2578) != ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2578) != ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2579) != ti(arrow_490897120le_alt,X2582)
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),X2580))
        | ti(arrow_490897120le_alt,X2579) != ti(arrow_490897120le_alt,X2582)
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2578) != ti(arrow_490897120le_alt,X2581)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2582),X2579)),X2580))
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),X2580))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2582),X2579)),X2580))
        | ti(arrow_490897120le_alt,X2579) = ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2579) != ti(arrow_490897120le_alt,X2581)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2582)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2578) != ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2581)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2582)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2581)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2582)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2578) != ti(arrow_490897120le_alt,X2581)
        | ti(arrow_490897120le_alt,X2579) != ti(arrow_490897120le_alt,X2582)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2582)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),X2580))
        | ti(arrow_490897120le_alt,X2579) != ti(arrow_490897120le_alt,X2582)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2582)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ti(arrow_490897120le_alt,X2578) != ti(arrow_490897120le_alt,X2581)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2582),X2579)),X2580))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2582)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),X2580))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2582),X2579)),X2580))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2582)),X2580))
        | ti(arrow_490897120le_alt,X2578) = ti(arrow_490897120le_alt,X2579)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2578),X2579)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2580),X2581),X2582)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2580),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2581) = ti(arrow_490897120le_alt,X2582) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_217_in__below])])]) ).

fof(i_0_632,plain,
    ! [X1999,X2000,X2001,X2002,X2003] :
      ( ( ti(arrow_490897120le_alt,X1999) != ti(arrow_490897120le_alt,X2000)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X1999) != ti(arrow_490897120le_alt,X2003)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2002),X2000)),X2001))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X2000) != ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2002)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2002)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X2000) = ti(arrow_490897120le_alt,X2003)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X1999) != ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X2000) != ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X2000) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),X2001))
        | ti(arrow_490897120le_alt,X2000) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X2000) != ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) != ti(arrow_490897120le_alt,X2002)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) != ti(arrow_490897120le_alt,X2002)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X2000) != ti(arrow_490897120le_alt,X2003)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2002)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),X2001))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2002)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X1999) != ti(arrow_490897120le_alt,X2003)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2002),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X2000) != ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X2000) = ti(arrow_490897120le_alt,X2003)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2002),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),X2001))
        | ti(arrow_490897120le_alt,X2000) = ti(arrow_490897120le_alt,X2003)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2002),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X2000) != ti(arrow_490897120le_alt,X2003)
        | ti(arrow_490897120le_alt,X1999) != ti(arrow_490897120le_alt,X2002)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2002),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) != ti(arrow_490897120le_alt,X2002)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2002),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ti(arrow_490897120le_alt,X2000) != ti(arrow_490897120le_alt,X2003)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2002)),X2001))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2002),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),X2001))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2002)),X2001))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2002),X2000)),X2001))
        | ti(arrow_490897120le_alt,X1999) = ti(arrow_490897120le_alt,X2000)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1999),X2000)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X2001),X2002),X2003)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2001),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2002) = ti(arrow_490897120le_alt,X2003) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_in__above])])]) ).

fof(i_0_633,plain,
    ! [X2004,X2005,X2006,X2007,X2010,X2011,X2012,X2013,X2014,X2015,X2016,X2017] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(X2004,X2005),bool),bool,hAPP(product_prod(X2004,X2005),fun(fun(product_prod(X2004,X2005),bool),bool),member(product_prod(X2004,X2005)),hAPP(X2005,product_prod(X2004,X2005),hAPP(X2004,fun(X2005,product_prod(X2004,X2005)),product_Pair(X2004,X2005),esk21_4(X2004,X2005,X2006,X2007)),esk22_4(X2004,X2005,X2006,X2007))),X2007))
        | ~ hBOOL(hAPP(fun(product_prod(X2004,X2005),bool),bool,hAPP(product_prod(X2004,X2005),fun(fun(product_prod(X2004,X2005),bool),bool),member(product_prod(X2004,X2005)),hAPP(X2005,product_prod(X2004,X2005),hAPP(X2004,fun(X2005,product_prod(X2004,X2005)),product_Pair(X2004,X2005),esk21_4(X2004,X2005,X2006,X2007)),esk22_4(X2004,X2005,X2006,X2007))),X2006))
        | ti(fun(product_prod(X2004,X2005),bool),X2007) = ti(fun(product_prod(X2004,X2005),bool),X2006) )
      & ( hBOOL(hAPP(fun(product_prod(X2004,X2005),bool),bool,hAPP(product_prod(X2004,X2005),fun(fun(product_prod(X2004,X2005),bool),bool),member(product_prod(X2004,X2005)),hAPP(X2005,product_prod(X2004,X2005),hAPP(X2004,fun(X2005,product_prod(X2004,X2005)),product_Pair(X2004,X2005),esk21_4(X2004,X2005,X2006,X2007)),esk22_4(X2004,X2005,X2006,X2007))),X2007))
        | hBOOL(hAPP(fun(product_prod(X2004,X2005),bool),bool,hAPP(product_prod(X2004,X2005),fun(fun(product_prod(X2004,X2005),bool),bool),member(product_prod(X2004,X2005)),hAPP(X2005,product_prod(X2004,X2005),hAPP(X2004,fun(X2005,product_prod(X2004,X2005)),product_Pair(X2004,X2005),esk21_4(X2004,X2005,X2006,X2007)),esk22_4(X2004,X2005,X2006,X2007))),X2006))
        | ti(fun(product_prod(X2004,X2005),bool),X2007) = ti(fun(product_prod(X2004,X2005),bool),X2006) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X2010,X2011),bool),bool,hAPP(product_prod(X2010,X2011),fun(fun(product_prod(X2010,X2011),bool),bool),member(product_prod(X2010,X2011)),hAPP(X2011,product_prod(X2010,X2011),hAPP(X2010,fun(X2011,product_prod(X2010,X2011)),product_Pair(X2010,X2011),X2014),X2015)),X2013))
        | hBOOL(hAPP(fun(product_prod(X2010,X2011),bool),bool,hAPP(product_prod(X2010,X2011),fun(fun(product_prod(X2010,X2011),bool),bool),member(product_prod(X2010,X2011)),hAPP(X2011,product_prod(X2010,X2011),hAPP(X2010,fun(X2011,product_prod(X2010,X2011)),product_Pair(X2010,X2011),X2014),X2015)),X2012))
        | ti(fun(product_prod(X2010,X2011),bool),X2013) != ti(fun(product_prod(X2010,X2011),bool),X2012) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X2010,X2011),bool),bool,hAPP(product_prod(X2010,X2011),fun(fun(product_prod(X2010,X2011),bool),bool),member(product_prod(X2010,X2011)),hAPP(X2011,product_prod(X2010,X2011),hAPP(X2010,fun(X2011,product_prod(X2010,X2011)),product_Pair(X2010,X2011),X2016),X2017)),X2012))
        | hBOOL(hAPP(fun(product_prod(X2010,X2011),bool),bool,hAPP(product_prod(X2010,X2011),fun(fun(product_prod(X2010,X2011),bool),bool),member(product_prod(X2010,X2011)),hAPP(X2011,product_prod(X2010,X2011),hAPP(X2010,fun(X2011,product_prod(X2010,X2011)),product_Pair(X2010,X2011),X2016),X2017)),X2013))
        | ti(fun(product_prod(X2010,X2011),bool),X2013) != ti(fun(product_prod(X2010,X2011),bool),X2012) ) ),
    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_79_pred__equals__eq2])])])])])]) ).

fof(i_0_634,plain,
    ! [X2829,X2830,X2831,X2832,X2833,X2834,X2835] :
      ( ~ hBOOL(hAPP(fun(fun(X2829,bool),X2830),bool,hAPP(fun(X2829,X2830),fun(fun(fun(X2829,bool),X2830),bool),hAPP(X2830,fun(fun(X2829,X2830),fun(fun(fun(X2829,bool),X2830),bool)),hAPP(fun(X2830,fun(X2830,X2830)),fun(X2830,fun(fun(X2829,X2830),fun(fun(fun(X2829,bool),X2830),bool))),finite908156982e_idem(X2830,X2829),X2832),X2833),X2834),X2835))
      | hAPP(X2830,X2830,hAPP(X2830,fun(X2830,X2830),X2832,X2831),X2831) = ti(X2830,X2831) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_305_folding__image__simple__idem_Oidem])]) ).

fof(i_0_635,plain,
    ! [X2629,X2630,X2631] :
      ( ti(arrow_490897120le_alt,X2630) = ti(arrow_490897120le_alt,X2631)
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X2629),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X2629),X2630),X2631)),arrow_2064824852le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_238_below__Lin])]) ).

fof(i_0_636,plain,
    ! [X1912,X1913,X1914] :
      ( ti(arrow_490897120le_alt,X1913) = ti(arrow_490897120le_alt,X1914)
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1912),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X1912),X1913),X1914)),arrow_2064824852le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_above__Lin])]) ).

fof(i_0_637,plain,
    ! [X3,X1,X37,X39] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39))),hAPP(fun(X1,bool),nat,finite_card(X1),X39)))
     => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X37),X39)) ),
    inference(fof_simplification,[status(thm)],[fact_472_pigeonhole]) ).

fof(i_0_638,plain,
    ! [X1902,X1903,X1904] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1902),X1903)),X1904))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1903),X1902)),X1904))
        | ti(arrow_490897120le_alt,X1902) = ti(arrow_490897120le_alt,X1903)
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1904),arrow_2064824852le_Lin)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1903),X1902)),X1904))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1902),X1903)),X1904))
        | ti(arrow_490897120le_alt,X1902) = ti(arrow_490897120le_alt,X1903)
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1904),arrow_2064824852le_Lin)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_609])])]) ).

fof(i_0_639,plain,
    ! [X14,X15,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X8))
       => ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),X8)) ) ),
    inference(fof_simplification,[status(thm)],[fact_47_Lin__irrefl]) ).

fof(i_0_640,plain,
    ! [X1790,X1791,X1792,X1793] :
      ( ( ti(arrow_490897120le_alt,X1791) != ti(arrow_490897120le_alt,X1793)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1792),X1793))) )
      & ( ti(arrow_490897120le_alt,X1790) != ti(arrow_490897120le_alt,X1793)
        | ti(arrow_490897120le_alt,X1790) != ti(arrow_490897120le_alt,X1791)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1792),X1793))) )
      & ( ti(arrow_490897120le_alt,X1790) = ti(arrow_490897120le_alt,X1793)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),X1792))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1792),X1793))) )
      & ( ti(arrow_490897120le_alt,X1790) != ti(arrow_490897120le_alt,X1793)
        | ti(arrow_490897120le_alt,X1790) = ti(arrow_490897120le_alt,X1793)
        | ti(arrow_490897120le_alt,X1791) = ti(arrow_490897120le_alt,X1793)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1792),X1793))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),X1792))
        | ti(arrow_490897120le_alt,X1790) = ti(arrow_490897120le_alt,X1793)
        | ti(arrow_490897120le_alt,X1791) = ti(arrow_490897120le_alt,X1793)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1792),X1793))) )
      & ( ti(arrow_490897120le_alt,X1790) != ti(arrow_490897120le_alt,X1793)
        | ti(arrow_490897120le_alt,X1790) = ti(arrow_490897120le_alt,X1791)
        | ti(arrow_490897120le_alt,X1791) = ti(arrow_490897120le_alt,X1793)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1792),X1793))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),X1792))
        | ti(arrow_490897120le_alt,X1790) = ti(arrow_490897120le_alt,X1791)
        | ti(arrow_490897120le_alt,X1791) = ti(arrow_490897120le_alt,X1793)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1790),X1791)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1792),X1793))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_in__mkbot])])]) ).

fof(i_0_641,plain,
    ! [X1794,X1795,X1796,X1797] :
      ( ( ti(arrow_490897120le_alt,X1794) != ti(arrow_490897120le_alt,X1797)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1796),X1797))) )
      & ( ti(arrow_490897120le_alt,X1795) != ti(arrow_490897120le_alt,X1797)
        | ti(arrow_490897120le_alt,X1794) != ti(arrow_490897120le_alt,X1795)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1796),X1797))) )
      & ( ti(arrow_490897120le_alt,X1795) = ti(arrow_490897120le_alt,X1797)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),X1796))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1796),X1797))) )
      & ( ti(arrow_490897120le_alt,X1795) != ti(arrow_490897120le_alt,X1797)
        | ti(arrow_490897120le_alt,X1795) = ti(arrow_490897120le_alt,X1797)
        | ti(arrow_490897120le_alt,X1794) = ti(arrow_490897120le_alt,X1797)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1796),X1797))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),X1796))
        | ti(arrow_490897120le_alt,X1795) = ti(arrow_490897120le_alt,X1797)
        | ti(arrow_490897120le_alt,X1794) = ti(arrow_490897120le_alt,X1797)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1796),X1797))) )
      & ( ti(arrow_490897120le_alt,X1795) != ti(arrow_490897120le_alt,X1797)
        | ti(arrow_490897120le_alt,X1794) = ti(arrow_490897120le_alt,X1795)
        | ti(arrow_490897120le_alt,X1794) = ti(arrow_490897120le_alt,X1797)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1796),X1797))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),X1796))
        | ti(arrow_490897120le_alt,X1794) = ti(arrow_490897120le_alt,X1795)
        | ti(arrow_490897120le_alt,X1794) = ti(arrow_490897120le_alt,X1797)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1794),X1795)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1796),X1797))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_in__mktop])])]) ).

fof(i_0_642,plain,
    ! [X3256,X3257,X3258,X3259,X3260,X3261] :
      ( hAPP(X3256,X3257,hAPP(fun(X3257,X3256),fun(X3256,X3257),hAPP(fun(X3257,bool),fun(fun(X3257,X3256),fun(X3256,X3257)),hilbert_inv_into(X3257,X3256),X3258),X3259),X3260) != hAPP(X3256,X3257,hAPP(fun(X3257,X3256),fun(X3256,X3257),hAPP(fun(X3257,bool),fun(fun(X3257,X3256),fun(X3256,X3257)),hilbert_inv_into(X3257,X3256),X3258),X3259),X3261)
      | ~ hBOOL(hAPP(fun(X3256,bool),bool,hAPP(X3256,fun(fun(X3256,bool),bool),member(X3256),X3260),hAPP(fun(X3257,bool),fun(X3256,bool),hAPP(fun(X3257,X3256),fun(fun(X3257,bool),fun(X3256,bool)),image(X3257,X3256),X3259),X3258)))
      | ~ hBOOL(hAPP(fun(X3256,bool),bool,hAPP(X3256,fun(fun(X3256,bool),bool),member(X3256),X3261),hAPP(fun(X3257,bool),fun(X3256,bool),hAPP(fun(X3257,X3256),fun(fun(X3257,bool),fun(X3256,bool)),image(X3257,X3256),X3259),X3258)))
      | ti(X3256,X3260) = ti(X3256,X3261) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_477_inv__into__injective])]) ).

fof(i_0_643,plain,
    ! [X3221,X3222,X3223] :
      ( ~ hBOOL(hAPP(fun(X3221,bool),bool,finite_finite_1(X3221),X3223))
      | ~ hBOOL(hAPP(fun(X3221,bool),bool,hAPP(fun(X3221,bool),fun(fun(X3221,bool),bool),ord_less_eq(fun(X3221,bool)),hAPP(fun(X3221,bool),fun(X3221,bool),hAPP(fun(X3221,X3221),fun(fun(X3221,bool),fun(X3221,bool)),image(X3221,X3221),X3222),X3223)),X3223))
      | ~ hBOOL(hAPP(fun(X3221,bool),bool,hAPP(fun(X3221,X3221),fun(fun(X3221,bool),bool),inj_on(X3221,X3221),X3222),X3223))
      | hAPP(fun(X3221,bool),fun(X3221,bool),hAPP(fun(X3221,X3221),fun(fun(X3221,bool),fun(X3221,bool)),image(X3221,X3221),X3222),X3223) = ti(fun(X3221,bool),X3223) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_465_endo__inj__surj])]) ).

fof(i_0_644,plain,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
     => ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,fun(X1,bool),X43,X6)))
       => ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39)) ) ),
    inference(fof_simplification,[status(thm)],[fact_86_PiE]) ).

fof(i_0_645,plain,
    ! [X3361,X3362,X3363,X3364] :
      ( hAPP(fun(X3361,bool),fun(X3362,bool),hAPP(fun(X3361,X3362),fun(fun(X3361,bool),fun(X3362,bool)),image(X3361,X3362),X3364),top_top(fun(X3361,bool))) != top_top(fun(X3362,bool))
      | hAPP(fun(X3361,bool),fun(X3362,bool),hAPP(fun(X3361,X3362),fun(fun(X3361,bool),fun(X3362,bool)),image(X3361,X3362),X3364),hAPP(fun(X3362,bool),fun(X3361,bool),hAPP(fun(X3362,X3361),fun(fun(X3362,bool),fun(X3361,bool)),image(X3362,X3361),hAPP(fun(X3361,X3362),fun(X3362,X3361),hAPP(fun(X3361,bool),fun(fun(X3361,X3362),fun(X3362,X3361)),hilbert_inv_into(X3361,X3362),top_top(fun(X3361,bool))),X3364)),X3363)) = ti(fun(X3362,bool),X3363) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_496_image__surj__f__inv__f])]) ).

fof(i_0_646,plain,
    ! [X3267,X3268,X3269,X3270,X3271] :
      ( ~ hBOOL(hAPP(fun(X3267,bool),bool,hAPP(X3267,fun(fun(X3267,bool),bool),member(X3267),X3269),hAPP(fun(X3268,bool),fun(X3267,bool),hAPP(fun(X3268,X3267),fun(fun(X3268,bool),fun(X3267,bool)),image(X3268,X3267),X3270),X3271)))
      | hAPP(X3268,X3267,X3270,hAPP(X3267,X3268,hAPP(fun(X3268,X3267),fun(X3267,X3268),hAPP(fun(X3268,bool),fun(fun(X3268,X3267),fun(X3267,X3268)),hilbert_inv_into(X3268,X3267),X3271),X3270),X3269)) = ti(X3267,X3269) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_479_f__inv__into__f])]) ).

fof(i_0_647,plain,
    ! [X3303,X3304,X3305,X3306,X3307,X3309,X3310,X3311,X3312,X3313,X3314] :
      ( ( hBOOL(hAPP(fun(X3304,bool),bool,hAPP(fun(X3304,bool),fun(fun(X3304,bool),bool),ord_less_eq(fun(X3304,bool)),esk102_5(X3303,X3304,X3305,X3306,X3307)),X3307))
        | ~ hBOOL(hAPP(fun(X3303,bool),bool,hAPP(fun(X3303,bool),fun(fun(X3303,bool),bool),ord_less_eq(fun(X3303,bool)),X3305),hAPP(fun(X3304,bool),fun(X3303,bool),hAPP(fun(X3304,X3303),fun(fun(X3304,bool),fun(X3303,bool)),image(X3304,X3303),X3306),X3307))) )
      & ( ti(fun(X3303,bool),X3305) = hAPP(fun(X3304,bool),fun(X3303,bool),hAPP(fun(X3304,X3303),fun(fun(X3304,bool),fun(X3303,bool)),image(X3304,X3303),X3306),esk102_5(X3303,X3304,X3305,X3306,X3307))
        | ~ hBOOL(hAPP(fun(X3303,bool),bool,hAPP(fun(X3303,bool),fun(fun(X3303,bool),bool),ord_less_eq(fun(X3303,bool)),X3305),hAPP(fun(X3304,bool),fun(X3303,bool),hAPP(fun(X3304,X3303),fun(fun(X3304,bool),fun(X3303,bool)),image(X3304,X3303),X3306),X3307))) )
      & ( ~ hBOOL(hAPP(fun(X3310,bool),bool,hAPP(fun(X3310,bool),fun(fun(X3310,bool),bool),ord_less_eq(fun(X3310,bool)),X3314),X3313))
        | ti(fun(X3309,bool),X3311) != hAPP(fun(X3310,bool),fun(X3309,bool),hAPP(fun(X3310,X3309),fun(fun(X3310,bool),fun(X3309,bool)),image(X3310,X3309),X3312),X3314)
        | hBOOL(hAPP(fun(X3309,bool),bool,hAPP(fun(X3309,bool),fun(fun(X3309,bool),bool),ord_less_eq(fun(X3309,bool)),X3311),hAPP(fun(X3310,bool),fun(X3309,bool),hAPP(fun(X3310,X3309),fun(fun(X3310,bool),fun(X3309,bool)),image(X3310,X3309),X3312),X3313))) ) ),
    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_485_subset__image__iff])])])])])]) ).

fof(i_0_648,plain,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ) ),
    inference(fof_simplification,[status(thm)],[fact_218_add__leE]) ).

fof(i_0_649,plain,
    ! [X3283,X3284,X3285,X3286,X3287,X3289,X3290,X3291,X3292,X3293,X3294] :
      ( ( hBOOL(hAPP(fun(X3284,bool),bool,hAPP(X3284,fun(fun(X3284,bool),bool),member(X3284),esk101_5(X3283,X3284,X3285,X3286,X3287)),X3287))
        | ~ hBOOL(hAPP(fun(X3283,bool),bool,hAPP(X3283,fun(fun(X3283,bool),bool),member(X3283),X3285),hAPP(fun(X3284,bool),fun(X3283,bool),hAPP(fun(X3284,X3283),fun(fun(X3284,bool),fun(X3283,bool)),image(X3284,X3283),X3286),X3287))) )
      & ( ti(X3283,X3285) = hAPP(X3284,X3283,X3286,esk101_5(X3283,X3284,X3285,X3286,X3287))
        | ~ hBOOL(hAPP(fun(X3283,bool),bool,hAPP(X3283,fun(fun(X3283,bool),bool),member(X3283),X3285),hAPP(fun(X3284,bool),fun(X3283,bool),hAPP(fun(X3284,X3283),fun(fun(X3284,bool),fun(X3283,bool)),image(X3284,X3283),X3286),X3287))) )
      & ( ~ hBOOL(hAPP(fun(X3290,bool),bool,hAPP(X3290,fun(fun(X3290,bool),bool),member(X3290),X3294),X3293))
        | ti(X3289,X3291) != hAPP(X3290,X3289,X3292,X3294)
        | hBOOL(hAPP(fun(X3289,bool),bool,hAPP(X3289,fun(fun(X3289,bool),bool),member(X3289),X3291),hAPP(fun(X3290,bool),fun(X3289,bool),hAPP(fun(X3290,X3289),fun(fun(X3290,bool),fun(X3289,bool)),image(X3290,X3289),X3292),X3293))) ) ),
    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_482_image__iff])])])])])]) ).

fof(i_0_650,plain,
    ! [X2811,X2812,X2813] :
      ( ~ hBOOL(hAPP(fun(X2811,bool),bool,finite_finite_1(X2811),X2813))
      | ~ hBOOL(hAPP(fun(X2811,bool),bool,hAPP(fun(X2811,bool),fun(fun(X2811,bool),bool),ord_less_eq(fun(X2811,bool)),X2812),X2813))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X2811,bool),nat,finite_card(X2811),X2813)),hAPP(fun(X2811,bool),nat,finite_card(X2811),X2812)))
      | ti(fun(X2811,bool),X2812) = ti(fun(X2811,bool),X2813) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_300_card__seteq])]) ).

fof(i_0_651,plain,
    ! [X58,X59] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X58)),
    inference(fof_simplification,[status(thm)],[fact_240_not__add__less1]) ).

fof(i_0_652,plain,
    ! [X59,X58] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X58)),X58)),
    inference(fof_simplification,[status(thm)],[fact_241_not__add__less2]) ).

fof(i_0_653,plain,
    ! [X3,X39] :
      ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,hAPP(nat,fun(fun(X3,bool),nat),hAPP(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat))),finite_fold_image(nat,X3),plus_plus(nat)),hAPP(nat,fun(X3,nat),combk(nat,X3),one_one(nat))),zero_zero(nat)),X39) )
      & ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ) ),
    inference(fof_simplification,[status(thm)],[fact_455_card__def]) ).

fof(i_0_654,plain,
    ! [X2039,X2040] :
      ( ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk26_2(X2039,X2040)),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X2039) = ti(arrow_490897120le_alt,X2040) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2039),X2040)),esk26_2(X2039,X2040)))
        | ti(arrow_490897120le_alt,X2039) = ti(arrow_490897120le_alt,X2040) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_87_complete__Lin])])])]) ).

fof(i_0_655,plain,
    ! [X2209,X2210,X2211,X2212,X2213,X2214] :
      ( ( hAPP(X2209,X2210,X2213,X2212) != hAPP(X2209,X2210,X2213,X2211)
        | ti(X2209,X2212) = ti(X2209,X2211)
        | ~ hBOOL(hAPP(fun(X2209,bool),bool,hAPP(X2209,fun(fun(X2209,bool),bool),member(X2209),X2211),X2214))
        | ~ hBOOL(hAPP(fun(X2209,bool),bool,hAPP(X2209,fun(fun(X2209,bool),bool),member(X2209),X2212),X2214))
        | ~ hBOOL(hAPP(fun(X2209,bool),bool,hAPP(fun(X2209,X2210),fun(fun(X2209,bool),bool),inj_on(X2209,X2210),X2213),X2214)) )
      & ( ti(X2209,X2212) != ti(X2209,X2211)
        | hAPP(X2209,X2210,X2213,X2212) = hAPP(X2209,X2210,X2213,X2211)
        | ~ hBOOL(hAPP(fun(X2209,bool),bool,hAPP(X2209,fun(fun(X2209,bool),bool),member(X2209),X2211),X2214))
        | ~ hBOOL(hAPP(fun(X2209,bool),bool,hAPP(X2209,fun(fun(X2209,bool),bool),member(X2209),X2212),X2214))
        | ~ hBOOL(hAPP(fun(X2209,bool),bool,hAPP(fun(X2209,X2210),fun(fun(X2209,bool),bool),inj_on(X2209,X2210),X2213),X2214)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_135_inj__on__iff])])]) ).

fof(i_0_656,plain,
    ! [X2215,X2216,X2217,X2218,X2219,X2220] :
      ( ~ hBOOL(hAPP(fun(X2215,bool),bool,hAPP(fun(X2215,X2216),fun(fun(X2215,bool),bool),inj_on(X2215,X2216),X2219),X2220))
      | hAPP(X2215,X2216,X2219,X2217) != hAPP(X2215,X2216,X2219,X2218)
      | ~ hBOOL(hAPP(fun(X2215,bool),bool,hAPP(X2215,fun(fun(X2215,bool),bool),member(X2215),X2217),X2220))
      | ~ hBOOL(hAPP(fun(X2215,bool),bool,hAPP(X2215,fun(fun(X2215,bool),bool),member(X2215),X2218),X2220))
      | ti(X2215,X2217) = ti(X2215,X2218) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_inj__onD])]) ).

fof(i_0_657,plain,
    ! [X2203,X2204,X2205,X2206,X2207,X2208] :
      ( ~ hBOOL(hAPP(fun(X2203,bool),bool,hAPP(fun(X2203,X2204),fun(fun(X2203,bool),bool),inj_on(X2203,X2204),X2207),X2208))
      | ti(X2203,X2205) = ti(X2203,X2206)
      | ~ hBOOL(hAPP(fun(X2203,bool),bool,hAPP(X2203,fun(fun(X2203,bool),bool),member(X2203),X2205),X2208))
      | ~ hBOOL(hAPP(fun(X2203,bool),bool,hAPP(X2203,fun(fun(X2203,bool),bool),member(X2203),X2206),X2208))
      | hAPP(X2203,X2204,X2207,X2205) != hAPP(X2203,X2204,X2207,X2206) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_134_inj__on__contraD])]) ).

fof(i_0_658,plain,
    ! [X2191,X2192,X2193,X2194,X2195,X2196,X2197,X2198,X2199,X2200] :
      ( ( ~ hBOOL(hAPP(fun(X2191,bool),bool,hAPP(fun(X2191,X2192),fun(fun(X2191,bool),bool),inj_on(X2191,X2192),X2193),X2194))
        | ~ hBOOL(hAPP(fun(X2191,bool),bool,hAPP(X2191,fun(fun(X2191,bool),bool),member(X2191),X2195),X2194))
        | ~ hBOOL(hAPP(fun(X2191,bool),bool,hAPP(X2191,fun(fun(X2191,bool),bool),member(X2191),X2196),X2194))
        | hAPP(X2191,X2192,X2193,X2195) != hAPP(X2191,X2192,X2193,X2196)
        | ti(X2191,X2195) = ti(X2191,X2196) )
      & ( hBOOL(hAPP(fun(X2197,bool),bool,hAPP(X2197,fun(fun(X2197,bool),bool),member(X2197),esk30_4(X2197,X2198,X2199,X2200)),X2200))
        | hBOOL(hAPP(fun(X2197,bool),bool,hAPP(fun(X2197,X2198),fun(fun(X2197,bool),bool),inj_on(X2197,X2198),X2199),X2200)) )
      & ( hBOOL(hAPP(fun(X2197,bool),bool,hAPP(X2197,fun(fun(X2197,bool),bool),member(X2197),esk31_4(X2197,X2198,X2199,X2200)),X2200))
        | hBOOL(hAPP(fun(X2197,bool),bool,hAPP(fun(X2197,X2198),fun(fun(X2197,bool),bool),inj_on(X2197,X2198),X2199),X2200)) )
      & ( hAPP(X2197,X2198,X2199,esk30_4(X2197,X2198,X2199,X2200)) = hAPP(X2197,X2198,X2199,esk31_4(X2197,X2198,X2199,X2200))
        | hBOOL(hAPP(fun(X2197,bool),bool,hAPP(fun(X2197,X2198),fun(fun(X2197,bool),bool),inj_on(X2197,X2198),X2199),X2200)) )
      & ( ti(X2197,esk30_4(X2197,X2198,X2199,X2200)) != ti(X2197,esk31_4(X2197,X2198,X2199,X2200))
        | hBOOL(hAPP(fun(X2197,bool),bool,hAPP(fun(X2197,X2198),fun(fun(X2197,bool),bool),inj_on(X2197,X2198),X2199),X2200)) ) ),
    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_133_inj__on__def])])])])])]) ).

fof(i_0_659,plain,
    ! [X3195,X3196,X3197,X3198,X3199,X3200] :
      ( ti(X3195,X3198) != hAPP(X3196,X3195,X3199,X3200)
      | ~ hBOOL(hAPP(fun(X3196,bool),bool,hAPP(X3196,fun(fun(X3196,bool),bool),member(X3196),X3200),X3197))
      | hBOOL(hAPP(fun(X3195,bool),bool,hAPP(X3195,fun(fun(X3195,bool),bool),member(X3195),X3198),hAPP(fun(X3196,bool),fun(X3195,bool),hAPP(fun(X3196,X3195),fun(fun(X3196,bool),fun(X3195,bool)),image(X3196,X3195),X3199),X3197))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_458_image__eqI])]) ).

fof(i_0_660,plain,
    ! [X3272,X3273,X3274,X3275,X3276,X3277] :
      ( ~ hBOOL(hAPP(fun(X3273,bool),bool,hAPP(X3273,fun(fun(X3273,bool),bool),member(X3273),X3276),X3277))
      | ti(X3272,X3274) != hAPP(X3273,X3272,X3275,X3276)
      | hBOOL(hAPP(fun(X3272,bool),bool,hAPP(X3272,fun(fun(X3272,bool),bool),member(X3272),X3274),hAPP(fun(X3273,bool),fun(X3272,bool),hAPP(fun(X3273,X3272),fun(fun(X3273,bool),fun(X3272,bool)),image(X3273,X3272),X3275),X3277))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_480_rev__image__eqI])]) ).

fof(i_0_661,plain,
    ~ ! [X31] :
        ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),X31))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X31),arrow_2064824852le_Lin)) ),
    inference(fof_simplification,[status(thm)],[fact_43__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_]) ).

fof(i_0_662,plain,
    ~ ! [X30] :
        ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),X30))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X30),arrow_2064824852le_Lin)) ),
    inference(fof_simplification,[status(thm)],[fact_42__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_]) ).

fof(i_0_663,plain,
    ! [X2258,X2259,X2260,X2261,X2262,X2263] :
      ( ~ hBOOL(hAPP(fun(X2258,bool),bool,hAPP(fun(X2258,X2259),fun(fun(X2258,bool),bool),inj_on(X2258,X2259),X2262),X2263))
      | ~ hBOOL(hAPP(fun(X2258,bool),bool,hAPP(X2258,fun(fun(X2258,bool),bool),member(X2258),X2261),X2263))
      | hAPP(X2258,X2259,X2262,X2261) != ti(X2259,X2260)
      | hAPP(X2259,X2258,hAPP(fun(X2258,X2259),fun(X2259,X2258),hAPP(fun(X2258,bool),fun(fun(X2258,X2259),fun(X2259,X2258)),hilbert_inv_into(X2258,X2259),X2263),X2262),X2260) = ti(X2258,X2261) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_inv__into__f__eq])]) ).

fof(i_0_664,plain,
    ! [X2253,X2254,X2255,X2256,X2257] :
      ( ~ hBOOL(hAPP(fun(X2253,bool),bool,hAPP(fun(X2253,X2254),fun(fun(X2253,bool),bool),inj_on(X2253,X2254),X2256),X2257))
      | ~ hBOOL(hAPP(fun(X2253,bool),bool,hAPP(X2253,fun(fun(X2253,bool),bool),member(X2253),X2255),X2257))
      | hAPP(X2254,X2253,hAPP(fun(X2253,X2254),fun(X2254,X2253),hAPP(fun(X2253,bool),fun(fun(X2253,X2254),fun(X2254,X2253)),hilbert_inv_into(X2253,X2254),X2257),X2256),hAPP(X2253,X2254,X2256,X2255)) = ti(X2253,X2255) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_145_inv__into__f__f])]) ).

fof(i_0_665,plain,
    ! [X2270,X2271,X2272,X2273] :
      ( ~ hBOOL(hAPP(fun(X2270,bool),bool,hAPP(fun(X2270,X2271),fun(fun(X2270,bool),bool),inj_on(X2270,X2271),X2273),top_top(fun(X2270,bool))))
      | hAPP(X2270,X2271,X2273,hAPP(X2271,X2270,X2272,esk34_4(X2270,X2271,X2272,X2273))) != ti(X2271,esk34_4(X2270,X2271,X2272,X2273))
      | hAPP(fun(X2270,X2271),fun(X2271,X2270),hAPP(fun(X2270,bool),fun(fun(X2270,X2271),fun(X2271,X2270)),hilbert_inv_into(X2270,X2271),top_top(fun(X2270,bool))),X2273) = ti(fun(X2271,X2270),X2272) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_148_inj__imp__inv__eq])])]) ).

fof(i_0_666,plain,
    ! [X3320,X3321,X3322,X3323,X3324] :
      ( ( ti(X3320,X3323) = ti(X3320,X3321)
        | hAPP(X3320,fun(X3320,bool),hAPP(X3320,fun(X3320,fun(X3320,bool)),ord_atLeastLessThan(X3320),X3323),X3324) != hAPP(X3320,fun(X3320,bool),hAPP(X3320,fun(X3320,fun(X3320,bool)),ord_atLeastLessThan(X3320),X3321),X3322)
        | ~ hBOOL(hAPP(X3320,bool,hAPP(X3320,fun(X3320,bool),ord_less(X3320),X3321),X3322))
        | ~ hBOOL(hAPP(X3320,bool,hAPP(X3320,fun(X3320,bool),ord_less(X3320),X3323),X3324))
        | ~ linorder(X3320) )
      & ( ti(X3320,X3324) = ti(X3320,X3322)
        | hAPP(X3320,fun(X3320,bool),hAPP(X3320,fun(X3320,fun(X3320,bool)),ord_atLeastLessThan(X3320),X3323),X3324) != hAPP(X3320,fun(X3320,bool),hAPP(X3320,fun(X3320,fun(X3320,bool)),ord_atLeastLessThan(X3320),X3321),X3322)
        | ~ hBOOL(hAPP(X3320,bool,hAPP(X3320,fun(X3320,bool),ord_less(X3320),X3321),X3322))
        | ~ hBOOL(hAPP(X3320,bool,hAPP(X3320,fun(X3320,bool),ord_less(X3320),X3323),X3324))
        | ~ linorder(X3320) )
      & ( ti(X3320,X3323) != ti(X3320,X3321)
        | ti(X3320,X3324) != ti(X3320,X3322)
        | hAPP(X3320,fun(X3320,bool),hAPP(X3320,fun(X3320,fun(X3320,bool)),ord_atLeastLessThan(X3320),X3323),X3324) = hAPP(X3320,fun(X3320,bool),hAPP(X3320,fun(X3320,fun(X3320,bool)),ord_atLeastLessThan(X3320),X3321),X3322)
        | ~ hBOOL(hAPP(X3320,bool,hAPP(X3320,fun(X3320,bool),ord_less(X3320),X3321),X3322))
        | ~ hBOOL(hAPP(X3320,bool,hAPP(X3320,fun(X3320,bool),ord_less(X3320),X3323),X3324))
        | ~ linorder(X3320) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_487_atLeastLessThan__eq__iff])])])]) ).

fof(i_0_667,plain,
    ! [X3325,X3326,X3327,X3328,X3329] :
      ( ~ linorder(X3325)
      | hAPP(X3325,fun(X3325,bool),hAPP(X3325,fun(X3325,fun(X3325,bool)),ord_atLeastLessThan(X3325),X3326),X3327) != hAPP(X3325,fun(X3325,bool),hAPP(X3325,fun(X3325,fun(X3325,bool)),ord_atLeastLessThan(X3325),X3328),X3329)
      | ~ hBOOL(hAPP(X3325,bool,hAPP(X3325,fun(X3325,bool),ord_less(X3325),X3326),X3327))
      | ~ hBOOL(hAPP(X3325,bool,hAPP(X3325,fun(X3325,bool),ord_less(X3325),X3328),X3329))
      | ti(X3325,X3326) = ti(X3325,X3328) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_488_atLeastLessThan__inj_I1_J])])]) ).

fof(i_0_668,plain,
    ! [X3330,X3331,X3332,X3333,X3334] :
      ( ~ linorder(X3330)
      | hAPP(X3330,fun(X3330,bool),hAPP(X3330,fun(X3330,fun(X3330,bool)),ord_atLeastLessThan(X3330),X3331),X3332) != hAPP(X3330,fun(X3330,bool),hAPP(X3330,fun(X3330,fun(X3330,bool)),ord_atLeastLessThan(X3330),X3333),X3334)
      | ~ hBOOL(hAPP(X3330,bool,hAPP(X3330,fun(X3330,bool),ord_less(X3330),X3331),X3332))
      | ~ hBOOL(hAPP(X3330,bool,hAPP(X3330,fun(X3330,bool),ord_less(X3330),X3333),X3334))
      | ti(X3330,X3332) = ti(X3330,X3334) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_489_atLeastLessThan__inj_I2_J])])]) ).

fof(i_0_669,plain,
    ! [X54,X29] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),X54)) ),
    inference(fof_simplification,[status(thm)],[fact_378_not__less__eq__eq]) ).

fof(i_0_670,plain,
    ! [X1743,X1744] : ti(fun(fun(X1743,fun(X1743,X1743)),fun(X1743,fun(fun(X1744,X1743),fun(fun(fun(X1744,bool),X1743),bool)))),finite908156982e_idem(X1743,X1744)) = finite908156982e_idem(X1743,X1744),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__image__simple__idem_res]) ).

fof(i_0_671,plain,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less(fun(X3,X1)),X37),X38))
        <=> ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
            & ~ hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X38),X37)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_155_less__fun__def]) ).

fof(i_0_672,plain,
    ! [X3340,X3341,X3342,X3343,X3344] :
      ( ti(X3340,X3342) != hAPP(X3341,X3340,X3343,X3344)
      | hBOOL(hAPP(fun(X3340,bool),bool,hAPP(X3340,fun(fun(X3340,bool),bool),member(X3340),X3342),hAPP(fun(X3341,bool),fun(X3340,bool),hAPP(fun(X3341,X3340),fun(fun(X3341,bool),fun(X3340,bool)),image(X3341,X3340),X3343),top_top(fun(X3341,bool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_491_range__eqI])]) ).

fof(i_0_673,plain,
    ! [X2522,X2523,X2524] :
      ( ( hBOOL(hAPP(fun(X2522,bool),bool,hAPP(fun(X2522,bool),fun(fun(X2522,bool),bool),ord_less_eq(fun(X2522,bool)),X2523),X2524))
        | ti(fun(X2522,bool),X2523) != ti(fun(X2522,bool),X2524) )
      & ( hBOOL(hAPP(fun(X2522,bool),bool,hAPP(fun(X2522,bool),fun(fun(X2522,bool),bool),ord_less_eq(fun(X2522,bool)),X2524),X2523))
        | ti(fun(X2522,bool),X2523) != ti(fun(X2522,bool),X2524) )
      & ( ~ hBOOL(hAPP(fun(X2522,bool),bool,hAPP(fun(X2522,bool),fun(fun(X2522,bool),bool),ord_less_eq(fun(X2522,bool)),X2523),X2524))
        | ~ hBOOL(hAPP(fun(X2522,bool),bool,hAPP(fun(X2522,bool),fun(fun(X2522,bool),bool),ord_less_eq(fun(X2522,bool)),X2524),X2523))
        | ti(fun(X2522,bool),X2523) = ti(fun(X2522,bool),X2524) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_206_set__eq__subset])])]) ).

fof(i_0_674,plain,
    ! [X2453,X2454,X2455] :
      ( ~ hBOOL(hAPP(fun(X2453,bool),bool,hAPP(fun(X2453,bool),fun(fun(X2453,bool),bool),ord_less_eq(fun(X2453,bool)),X2454),X2455))
      | ~ hBOOL(hAPP(fun(X2453,bool),bool,hAPP(fun(X2453,bool),fun(fun(X2453,bool),bool),ord_less_eq(fun(X2453,bool)),X2455),X2454))
      | ti(fun(X2453,bool),X2454) = ti(fun(X2453,bool),X2455) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_188_equalityI])]) ).

fof(i_0_675,plain,
    ! [X2019,X2020,X2021,X2022,X2023] :
      ( ~ hBOOL(hAPP(fun(X2019,bool),bool,hAPP(fun(X2019,X2020),fun(fun(X2019,bool),bool),inj_on(X2019,X2020),X2023),top_top(fun(X2019,bool))))
      | hAPP(X2019,X2020,X2023,X2021) != ti(X2020,X2022)
      | hAPP(X2020,X2019,hAPP(fun(X2019,X2020),fun(X2020,X2019),hAPP(fun(X2019,bool),fun(fun(X2019,X2020),fun(X2020,X2019)),hilbert_inv_into(X2019,X2020),top_top(fun(X2019,bool))),X2023),X2022) = ti(X2019,X2021) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_83_inv__f__eq])]) ).

fof(i_0_676,plain,
    ! [X2024,X2025,X2026,X2027] :
      ( ~ hBOOL(hAPP(fun(X2024,bool),bool,hAPP(fun(X2024,X2025),fun(fun(X2024,bool),bool),inj_on(X2024,X2025),X2027),top_top(fun(X2024,bool))))
      | hAPP(X2025,X2024,hAPP(fun(X2024,X2025),fun(X2025,X2024),hAPP(fun(X2024,bool),fun(fun(X2024,X2025),fun(X2025,X2024)),hilbert_inv_into(X2024,X2025),top_top(fun(X2024,bool))),X2027),hAPP(X2024,X2025,X2027,X2026)) = ti(X2024,X2026) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_84_inv__f__f])]) ).

fof(i_0_677,plain,
    ! [X2927,X2928,X2929] :
      ( ( ti(X2927,X2929) = zero_zero(X2927)
        | hAPP(X2927,X2927,hAPP(X2927,fun(X2927,X2927),plus_plus(X2927),X2929),X2928) != zero_zero(X2927)
        | ~ hBOOL(hAPP(X2927,bool,hAPP(X2927,fun(X2927,bool),ord_less_eq(X2927),zero_zero(X2927)),X2928))
        | ~ hBOOL(hAPP(X2927,bool,hAPP(X2927,fun(X2927,bool),ord_less_eq(X2927),zero_zero(X2927)),X2929))
        | ~ ordere216010020id_add(X2927) )
      & ( ti(X2927,X2928) = zero_zero(X2927)
        | hAPP(X2927,X2927,hAPP(X2927,fun(X2927,X2927),plus_plus(X2927),X2929),X2928) != zero_zero(X2927)
        | ~ hBOOL(hAPP(X2927,bool,hAPP(X2927,fun(X2927,bool),ord_less_eq(X2927),zero_zero(X2927)),X2928))
        | ~ hBOOL(hAPP(X2927,bool,hAPP(X2927,fun(X2927,bool),ord_less_eq(X2927),zero_zero(X2927)),X2929))
        | ~ ordere216010020id_add(X2927) )
      & ( ti(X2927,X2929) != zero_zero(X2927)
        | ti(X2927,X2928) != zero_zero(X2927)
        | hAPP(X2927,X2927,hAPP(X2927,fun(X2927,X2927),plus_plus(X2927),X2929),X2928) = zero_zero(X2927)
        | ~ hBOOL(hAPP(X2927,bool,hAPP(X2927,fun(X2927,bool),ord_less_eq(X2927),zero_zero(X2927)),X2928))
        | ~ hBOOL(hAPP(X2927,bool,hAPP(X2927,fun(X2927,bool),ord_less_eq(X2927),zero_zero(X2927)),X2929))
        | ~ ordere216010020id_add(X2927) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_342_add__nonneg__eq__0__iff])])])]) ).

fof(i_0_678,plain,
    ! [X54,X29] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54))) ),
    inference(fof_simplification,[status(thm)],[fact_391_not__less__eq]) ).

fof(i_0_679,plain,
    ! [X2463,X2464,X2465] :
      ( ( ~ hBOOL(hAPP(fun(X2463,bool),bool,hAPP(fun(X2463,bool),fun(fun(X2463,bool),bool),ord_less_eq(fun(X2463,bool)),X2464),X2465))
        | hBOOL(hAPP(fun(X2463,bool),bool,hAPP(fun(X2463,bool),fun(fun(X2463,bool),bool),ord_less(fun(X2463,bool)),X2464),X2465))
        | ti(fun(X2463,bool),X2464) = ti(fun(X2463,bool),X2465) )
      & ( ~ hBOOL(hAPP(fun(X2463,bool),bool,hAPP(fun(X2463,bool),fun(fun(X2463,bool),bool),ord_less(fun(X2463,bool)),X2464),X2465))
        | hBOOL(hAPP(fun(X2463,bool),bool,hAPP(fun(X2463,bool),fun(fun(X2463,bool),bool),ord_less_eq(fun(X2463,bool)),X2464),X2465)) )
      & ( ti(fun(X2463,bool),X2464) != ti(fun(X2463,bool),X2465)
        | hBOOL(hAPP(fun(X2463,bool),bool,hAPP(fun(X2463,bool),fun(fun(X2463,bool),bool),ord_less_eq(fun(X2463,bool)),X2464),X2465)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_191_subset__iff__psubset__eq])])]) ).

fof(i_0_680,plain,
    ! [X2460,X2461,X2462] :
      ( ( hBOOL(hAPP(fun(X2460,bool),bool,hAPP(fun(X2460,bool),fun(fun(X2460,bool),bool),ord_less_eq(fun(X2460,bool)),X2461),X2462))
        | ~ hBOOL(hAPP(fun(X2460,bool),bool,hAPP(fun(X2460,bool),fun(fun(X2460,bool),bool),ord_less(fun(X2460,bool)),X2461),X2462)) )
      & ( ti(fun(X2460,bool),X2461) != ti(fun(X2460,bool),X2462)
        | ~ hBOOL(hAPP(fun(X2460,bool),bool,hAPP(fun(X2460,bool),fun(fun(X2460,bool),bool),ord_less(fun(X2460,bool)),X2461),X2462)) )
      & ( ~ hBOOL(hAPP(fun(X2460,bool),bool,hAPP(fun(X2460,bool),fun(fun(X2460,bool),bool),ord_less_eq(fun(X2460,bool)),X2461),X2462))
        | ti(fun(X2460,bool),X2461) = ti(fun(X2460,bool),X2462)
        | hBOOL(hAPP(fun(X2460,bool),bool,hAPP(fun(X2460,bool),fun(fun(X2460,bool),bool),ord_less(fun(X2460,bool)),X2461),X2462)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_190_psubset__eq])])]) ).

fof(i_0_681,plain,
    ! [X2157,X2158,X2159] :
      ( ( hBOOL(hAPP(X2157,bool,hAPP(X2157,fun(X2157,bool),ord_less(X2157),X2158),X2159))
        | ti(X2157,X2158) = ti(X2157,X2159)
        | ~ hBOOL(hAPP(X2157,bool,hAPP(X2157,fun(X2157,bool),ord_less_eq(X2157),X2158),X2159))
        | ~ linorder(X2157) )
      & ( ti(X2157,X2158) != ti(X2157,X2159)
        | ~ hBOOL(hAPP(X2157,bool,hAPP(X2157,fun(X2157,bool),ord_less(X2157),X2158),X2159))
        | ~ hBOOL(hAPP(X2157,bool,hAPP(X2157,fun(X2157,bool),ord_less_eq(X2157),X2158),X2159))
        | ~ linorder(X2157) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_610])])])]) ).

fof(i_0_682,plain,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,suc,X53)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
       => X51 = hAPP(nat,nat,suc,X53) ) ),
    inference(fof_simplification,[status(thm)],[fact_382_le__SucE]) ).

fof(i_0_683,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_113_less__le__not__le]) ).

fof(i_0_684,plain,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
       => X51 = X53 ) ),
    inference(fof_simplification,[status(thm)],[fact_399_less__SucE]) ).

fof(i_0_685,plain,
    ! [X53,X51] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X51))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,suc,X51)))
       => X51 = X53 ) ),
    inference(fof_simplification,[status(thm)],[fact_395_less__antisym]) ).

fof(i_0_686,plain,
    ! [X29,X54] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54)))
      <=> X29 = X54 ) ),
    inference(fof_simplification,[status(thm)],[fact_394_not__less__less__Suc__eq]) ).

fof(i_0_687,plain,
    ! [X2104,X2105,X2106] :
      ( ( hBOOL(hAPP(X2104,bool,hAPP(X2104,fun(X2104,bool),ord_less_eq(X2104),X2105),X2106))
        | ti(X2104,X2105) != ti(X2104,X2106)
        | ~ order(X2104) )
      & ( hBOOL(hAPP(X2104,bool,hAPP(X2104,fun(X2104,bool),ord_less_eq(X2104),X2106),X2105))
        | ti(X2104,X2105) != ti(X2104,X2106)
        | ~ order(X2104) )
      & ( ~ hBOOL(hAPP(X2104,bool,hAPP(X2104,fun(X2104,bool),ord_less_eq(X2104),X2105),X2106))
        | ~ hBOOL(hAPP(X2104,bool,hAPP(X2104,fun(X2104,bool),ord_less_eq(X2104),X2106),X2105))
        | ti(X2104,X2105) = ti(X2104,X2106)
        | ~ order(X2104) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_106_order__eq__iff])])])]) ).

fof(i_0_688,plain,
    ! [X2093,X2094,X2095] :
      ( ( ~ hBOOL(hAPP(X2093,bool,hAPP(X2093,fun(X2093,bool),ord_less_eq(X2093),X2095),X2094))
        | ti(X2093,X2095) = ti(X2093,X2094)
        | ~ hBOOL(hAPP(X2093,bool,hAPP(X2093,fun(X2093,bool),ord_less_eq(X2093),X2094),X2095))
        | ~ order(X2093) )
      & ( ti(X2093,X2095) != ti(X2093,X2094)
        | hBOOL(hAPP(X2093,bool,hAPP(X2093,fun(X2093,bool),ord_less_eq(X2093),X2095),X2094))
        | ~ hBOOL(hAPP(X2093,bool,hAPP(X2093,fun(X2093,bool),ord_less_eq(X2093),X2094),X2095))
        | ~ order(X2093) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_103_order__antisym__conv])])])]) ).

fof(i_0_689,plain,
    ! [X2074,X2075,X2076] :
      ( ~ order(X2074)
      | ~ hBOOL(hAPP(X2074,bool,hAPP(X2074,fun(X2074,bool),ord_less_eq(X2074),X2075),X2076))
      | ~ hBOOL(hAPP(X2074,bool,hAPP(X2074,fun(X2074,bool),ord_less_eq(X2074),X2076),X2075))
      | ti(X2074,X2075) = ti(X2074,X2076) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_order__antisym])])]) ).

fof(i_0_690,plain,
    ! [X2067,X2068,X2069] :
      ( ~ order(X2067)
      | ~ hBOOL(hAPP(X2067,bool,hAPP(X2067,fun(X2067,bool),ord_less_eq(X2067),X2068),X2069))
      | ~ hBOOL(hAPP(X2067,bool,hAPP(X2067,fun(X2067,bool),ord_less_eq(X2067),X2069),X2068))
      | ti(X2067,X2069) = ti(X2067,X2068) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_xt1_I5_J])])]) ).

fof(i_0_691,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X53)),X53)),
    inference(fof_simplification,[status(thm)],[fact_377_Suc__n__not__le__n]) ).

fof(i_0_692,plain,
    ! [X29,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X29))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X29))
            & ! [X16] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X62))
               => ~ hBOOL(hAPP(nat,bool,X11,X16)) )
            & hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),one_one(nat)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_366_ex__least__nat__less]) ).

fof(i_0_693,plain,
    ! [X3] :
      ( order(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_60_xt1_I9_J]) ).

fof(i_0_694,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_66_order__less__not__sym]) ).

fof(i_0_695,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_65_order__less__imp__not__less]) ).

fof(i_0_696,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_61_order__less__asym_H]) ).

fof(i_0_697,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_53_order__less__asym]) ).

fof(i_0_698,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_110_linorder__not__le]) ).

fof(i_0_699,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_120_leD]) ).

fof(i_0_700,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_109_linorder__not__less]) ).

fof(i_0_701,plain,
    ! [X2085,X2086,X2087,X2088] :
      ( ~ order(X2085)
      | ti(X2085,X2087) != ti(X2085,X2088)
      | ~ hBOOL(hAPP(X2085,bool,hAPP(X2085,fun(X2085,bool),ord_less_eq(X2085),X2086),X2088))
      | hBOOL(hAPP(X2085,bool,hAPP(X2085,fun(X2085,bool),ord_less_eq(X2085),X2086),X2087)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_101_xt1_I3_J])])]) ).

fof(i_0_702,plain,
    ! [X2077,X2078,X2079,X2080] :
      ( ~ order(X2077)
      | ~ hBOOL(hAPP(X2077,bool,hAPP(X2077,fun(X2077,bool),ord_less_eq(X2077),X2079),X2080))
      | ti(X2077,X2079) != ti(X2077,X2078)
      | hBOOL(hAPP(X2077,bool,hAPP(X2077,fun(X2077,bool),ord_less_eq(X2077),X2078),X2080)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_99_xt1_I4_J])])]) ).

fof(i_0_703,plain,
    ! [X1974,X1975,X1976] :
      ( ( hBOOL(hAPP(X1974,bool,hAPP(X1974,fun(X1974,bool),ord_less(X1974),X1976),X1975))
        | ti(X1974,X1976) = ti(X1974,X1975)
        | hBOOL(hAPP(X1974,bool,hAPP(X1974,fun(X1974,bool),ord_less(X1974),X1975),X1976))
        | ~ linorder(X1974) )
      & ( ti(X1974,X1976) != ti(X1974,X1975)
        | ~ hBOOL(hAPP(X1974,bool,hAPP(X1974,fun(X1974,bool),ord_less(X1974),X1976),X1975))
        | hBOOL(hAPP(X1974,bool,hAPP(X1974,fun(X1974,bool),ord_less(X1974),X1975),X1976))
        | ~ linorder(X1974) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_611])])])]) ).

fof(i_0_704,plain,
    ! [X1938,X1939,X1940,X1941] :
      ( ~ order(X1938)
      | ti(X1938,X1940) != ti(X1938,X1941)
      | ~ hBOOL(hAPP(X1938,bool,hAPP(X1938,fun(X1938,bool),ord_less(X1938),X1939),X1941))
      | hBOOL(hAPP(X1938,bool,hAPP(X1938,fun(X1938,bool),ord_less(X1938),X1939),X1940)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_58_xt1_I1_J])])]) ).

fof(i_0_705,plain,
    ! [X1930,X1931,X1932,X1933] :
      ( ~ order(X1930)
      | ~ hBOOL(hAPP(X1930,bool,hAPP(X1930,fun(X1930,bool),ord_less(X1930),X1932),X1933))
      | ti(X1930,X1932) != ti(X1930,X1931)
      | hBOOL(hAPP(X1930,bool,hAPP(X1930,fun(X1930,bool),ord_less(X1930),X1931),X1933)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_xt1_I2_J])])]) ).

fof(i_0_706,plain,
    ! [X2166,X2167,X2168] :
      ( ~ order(X2166)
      | ~ hBOOL(hAPP(X2166,bool,hAPP(X2166,fun(X2166,bool),ord_less_eq(X2166),X2167),X2168))
      | ti(X2166,X2168) = ti(X2166,X2167)
      | hBOOL(hAPP(X2166,bool,hAPP(X2166,fun(X2166,bool),ord_less(X2166),X2167),X2168)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_125_xt1_I11_J])])]) ).

fof(i_0_707,plain,
    ! [X2163,X2164,X2165] :
      ( ~ order(X2163)
      | ~ hBOOL(hAPP(X2163,bool,hAPP(X2163,fun(X2163,bool),ord_less_eq(X2163),X2164),X2165))
      | ti(X2163,X2164) = ti(X2163,X2165)
      | hBOOL(hAPP(X2163,bool,hAPP(X2163,fun(X2163,bool),ord_less(X2163),X2164),X2165)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_124_order__le__neq__trans])])]) ).

fof(i_0_708,plain,
    ! [X2160,X2161,X2162] :
      ( ~ order(X2160)
      | ~ hBOOL(hAPP(X2160,bool,hAPP(X2160,fun(X2160,bool),ord_less_eq(X2160),X2161),X2162))
      | hBOOL(hAPP(X2160,bool,hAPP(X2160,fun(X2160,bool),ord_less(X2160),X2161),X2162))
      | ti(X2160,X2161) = ti(X2160,X2162) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_123_order__le__imp__less__or__eq])])]) ).

fof(i_0_709,plain,
    ! [X2145,X2146,X2147] :
      ( ~ order(X2145)
      | ti(X2145,X2146) = ti(X2145,X2147)
      | ~ hBOOL(hAPP(X2145,bool,hAPP(X2145,fun(X2145,bool),ord_less_eq(X2145),X2146),X2147))
      | hBOOL(hAPP(X2145,bool,hAPP(X2145,fun(X2145,bool),ord_less(X2145),X2146),X2147)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_118_order__neq__le__trans])])]) ).

fof(i_0_710,plain,
    ! [X2133,X2134,X2135] :
      ( ( ~ hBOOL(hAPP(X2133,bool,hAPP(X2133,fun(X2133,bool),ord_less_eq(X2133),X2134),X2135))
        | hBOOL(hAPP(X2133,bool,hAPP(X2133,fun(X2133,bool),ord_less(X2133),X2134),X2135))
        | ti(X2133,X2134) = ti(X2133,X2135)
        | ~ order(X2133) )
      & ( ~ hBOOL(hAPP(X2133,bool,hAPP(X2133,fun(X2133,bool),ord_less(X2133),X2134),X2135))
        | hBOOL(hAPP(X2133,bool,hAPP(X2133,fun(X2133,bool),ord_less_eq(X2133),X2134),X2135))
        | ~ order(X2133) )
      & ( ti(X2133,X2134) != ti(X2133,X2135)
        | hBOOL(hAPP(X2133,bool,hAPP(X2133,fun(X2133,bool),ord_less_eq(X2133),X2134),X2135))
        | ~ order(X2133) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_114_order__le__less])])])]) ).

fof(i_0_711,plain,
    ! [X2127,X2128,X2129] :
      ( ( hBOOL(hAPP(X2127,bool,hAPP(X2127,fun(X2127,bool),ord_less_eq(X2127),X2128),X2129))
        | ~ hBOOL(hAPP(X2127,bool,hAPP(X2127,fun(X2127,bool),ord_less(X2127),X2128),X2129))
        | ~ order(X2127) )
      & ( ti(X2127,X2128) != ti(X2127,X2129)
        | ~ hBOOL(hAPP(X2127,bool,hAPP(X2127,fun(X2127,bool),ord_less(X2127),X2128),X2129))
        | ~ order(X2127) )
      & ( ~ hBOOL(hAPP(X2127,bool,hAPP(X2127,fun(X2127,bool),ord_less_eq(X2127),X2128),X2129))
        | ti(X2127,X2128) = ti(X2127,X2129)
        | hBOOL(hAPP(X2127,bool,hAPP(X2127,fun(X2127,bool),ord_less(X2127),X2128),X2129))
        | ~ order(X2127) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_112_order__less__le])])])]) ).

fof(i_0_712,plain,
    ! [X2142,X2143,X2144] :
      ( ( ~ hBOOL(hAPP(X2142,bool,hAPP(X2142,fun(X2142,bool),ord_less_eq(X2142),X2143),X2144))
        | ti(X2142,X2143) = ti(X2142,X2144)
        | hBOOL(hAPP(X2142,bool,hAPP(X2142,fun(X2142,bool),ord_less(X2142),X2143),X2144))
        | ~ linorder(X2142) )
      & ( ti(X2142,X2143) != ti(X2142,X2144)
        | hBOOL(hAPP(X2142,bool,hAPP(X2142,fun(X2142,bool),ord_less_eq(X2142),X2143),X2144))
        | hBOOL(hAPP(X2142,bool,hAPP(X2142,fun(X2142,bool),ord_less(X2142),X2143),X2144))
        | ~ linorder(X2142) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_612])])])]) ).

fof(i_0_713,plain,
    ! [X2148,X2149,X2150] :
      ( ~ order(X2148)
      | ti(X2148,X2149) = ti(X2148,X2150)
      | ~ hBOOL(hAPP(X2148,bool,hAPP(X2148,fun(X2148,bool),ord_less_eq(X2148),X2150),X2149))
      | hBOOL(hAPP(X2148,bool,hAPP(X2148,fun(X2148,bool),ord_less(X2148),X2150),X2149)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_119_xt1_I12_J])])]) ).

fof(i_0_714,plain,
    ! [X2243,X2244,X2245,X2246,X2247] :
      ( ( hAPP(X2243,X2244,X2247,X2245) != hAPP(X2243,X2244,X2247,X2246)
        | ti(X2243,X2245) = ti(X2243,X2246)
        | ~ hBOOL(hAPP(fun(X2243,bool),bool,hAPP(fun(X2243,X2244),fun(fun(X2243,bool),bool),inj_on(X2243,X2244),X2247),top_top(fun(X2243,bool)))) )
      & ( ti(X2243,X2245) != ti(X2243,X2246)
        | hAPP(X2243,X2244,X2247,X2245) = hAPP(X2243,X2244,X2247,X2246)
        | ~ hBOOL(hAPP(fun(X2243,bool),bool,hAPP(fun(X2243,X2244),fun(fun(X2243,bool),bool),inj_on(X2243,X2244),X2247),top_top(fun(X2243,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_143_inj__eq])])]) ).

fof(i_0_715,plain,
    ! [X2248,X2249,X2250,X2251,X2252] :
      ( ~ hBOOL(hAPP(fun(X2248,bool),bool,hAPP(fun(X2248,X2249),fun(fun(X2248,bool),bool),inj_on(X2248,X2249),X2252),top_top(fun(X2248,bool))))
      | hAPP(X2248,X2249,X2252,X2250) != hAPP(X2248,X2249,X2252,X2251)
      | ti(X2248,X2250) = ti(X2248,X2251) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_144_injD])]) ).

fof(i_0_716,plain,
    ! [X29,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X29))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X29))
            & ! [X16] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X62))
               => ~ hBOOL(hAPP(nat,bool,X11,X16)) )
            & hBOOL(hAPP(nat,bool,X11,X62)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_368_ex__least__nat__le]) ).

fof(i_0_717,plain,
    ! [X3,X39] :
      ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => ? [X19] : ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X19),X39)) ) ),
    inference(fof_simplification,[status(thm)],[fact_301_ex__new__if__finite]) ).

fof(i_0_718,plain,
    ! [X3249,X3250] :
      ( ( hAPP(X3249,X3249,hAPP(X3249,fun(X3249,X3249),plus_plus(X3249),X3250),X3250) != zero_zero(X3249)
        | ti(X3249,X3250) = zero_zero(X3249)
        | ~ hBOOL(hAPP(fun(X3249,bool),bool,hAPP(X3249,fun(fun(X3249,bool),bool),member(X3249),X3250),ring_1_Ints(X3249)))
        | ~ ring_char_0(X3249) )
      & ( ti(X3249,X3250) != zero_zero(X3249)
        | hAPP(X3249,X3249,hAPP(X3249,fun(X3249,X3249),plus_plus(X3249),X3250),X3250) = zero_zero(X3249)
        | ~ hBOOL(hAPP(fun(X3249,bool),bool,hAPP(X3249,fun(fun(X3249,bool),bool),member(X3249),X3250),ring_1_Ints(X3249)))
        | ~ ring_char_0(X3249) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_473_Ints__double__eq__0__iff])])])]) ).

fof(i_0_719,plain,
    ! [X2751,X2752,X2753,X2754] :
      ( ( hBOOL(hAPP(fun(X2752,bool),bool,hAPP(X2752,fun(fun(X2752,bool),bool),member(X2752),esk69_4(X2751,X2752,X2753,X2754)),X2754))
        | hBOOL(hAPP(fun(X2752,bool),bool,hAPP(fun(X2752,X2751),fun(fun(X2752,bool),bool),inj_on(X2752,X2751),X2753),X2754)) )
      & ( hBOOL(hAPP(fun(X2752,bool),bool,hAPP(X2752,fun(fun(X2752,bool),bool),member(X2752),esk70_4(X2751,X2752,X2753,X2754)),X2754))
        | hBOOL(hAPP(fun(X2752,bool),bool,hAPP(fun(X2752,X2751),fun(fun(X2752,bool),bool),inj_on(X2752,X2751),X2753),X2754)) )
      & ( hAPP(X2752,X2751,X2753,esk69_4(X2751,X2752,X2753,X2754)) = hAPP(X2752,X2751,X2753,esk70_4(X2751,X2752,X2753,X2754))
        | hBOOL(hAPP(fun(X2752,bool),bool,hAPP(fun(X2752,X2751),fun(fun(X2752,bool),bool),inj_on(X2752,X2751),X2753),X2754)) )
      & ( ti(X2752,esk69_4(X2751,X2752,X2753,X2754)) != ti(X2752,esk70_4(X2751,X2752,X2753,X2754))
        | hBOOL(hAPP(fun(X2752,bool),bool,hAPP(fun(X2752,X2751),fun(fun(X2752,bool),bool),inj_on(X2752,X2751),X2753),X2754)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_275_inj__onI])])])])]) ).

fof(i_0_720,plain,
    ! [X1742] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(X1742,nat),fun(nat,fun(fun(X1742,bool),nat)))),finite_fold_image(nat,X1742)) = finite_fold_image(nat,X1742),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofold__image_res]) ).

fof(i_0_721,plain,
    ! [X2321,X2322,X2323] :
      ( ~ linordered_idom(X2321)
      | ti(X2321,X2322) = ti(X2321,X2323)
      | hBOOL(hAPP(X2321,bool,hAPP(X2321,fun(X2321,bool),ord_less(X2321),X2322),X2323))
      | hBOOL(hAPP(X2321,bool,hAPP(X2321,fun(X2321,bool),ord_less(X2321),X2323),X2322)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_613])])]) ).

fof(i_0_722,plain,
    ! [X1983,X1984,X1985] :
      ( ( ti(X1983,X1984) = ti(X1983,X1985)
        | hBOOL(hAPP(X1983,bool,hAPP(X1983,fun(X1983,bool),ord_less(X1983),X1984),X1985))
        | hBOOL(hAPP(X1983,bool,hAPP(X1983,fun(X1983,bool),ord_less(X1983),X1985),X1984))
        | ~ linorder(X1983) )
      & ( ~ hBOOL(hAPP(X1983,bool,hAPP(X1983,fun(X1983,bool),ord_less(X1983),X1984),X1985))
        | ti(X1983,X1984) != ti(X1983,X1985)
        | ~ linorder(X1983) )
      & ( ~ hBOOL(hAPP(X1983,bool,hAPP(X1983,fun(X1983,bool),ord_less(X1983),X1985),X1984))
        | ti(X1983,X1984) != ti(X1983,X1985)
        | ~ linorder(X1983) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_linorder__neq__iff])])])]) ).

fof(i_0_723,plain,
    ! [X1980,X1981,X1982] :
      ( ( hBOOL(hAPP(X1980,bool,hAPP(X1980,fun(X1980,bool),ord_less(X1980),X1981),X1982))
        | hBOOL(hAPP(X1980,bool,hAPP(X1980,fun(X1980,bool),ord_less(X1980),X1982),X1981))
        | ti(X1980,X1981) = ti(X1980,X1982)
        | ~ linorder(X1980) )
      & ( ~ hBOOL(hAPP(X1980,bool,hAPP(X1980,fun(X1980,bool),ord_less(X1980),X1982),X1981))
        | ~ hBOOL(hAPP(X1980,bool,hAPP(X1980,fun(X1980,bool),ord_less(X1980),X1981),X1982))
        | ~ linorder(X1980) )
      & ( ti(X1980,X1981) != ti(X1980,X1982)
        | ~ hBOOL(hAPP(X1980,bool,hAPP(X1980,fun(X1980,bool),ord_less(X1980),X1981),X1982))
        | ~ linorder(X1980) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_614])])])]) ).

fof(i_0_724,plain,
    ! [X1977,X1978,X1979] :
      ( ~ linorder(X1977)
      | hBOOL(hAPP(X1977,bool,hAPP(X1977,fun(X1977,bool),ord_less(X1977),X1978),X1979))
      | ti(X1977,X1978) = ti(X1977,X1979)
      | hBOOL(hAPP(X1977,bool,hAPP(X1977,fun(X1977,bool),ord_less(X1977),X1979),X1978)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_70_linorder__less__linear])])]) ).

fof(i_0_725,plain,
    ! [X1971,X1972,X1973] :
      ( ~ linorder(X1971)
      | ti(X1971,X1972) = ti(X1971,X1973)
      | hBOOL(hAPP(X1971,bool,hAPP(X1971,fun(X1971,bool),ord_less(X1971),X1972),X1973))
      | hBOOL(hAPP(X1971,bool,hAPP(X1971,fun(X1971,bool),ord_less(X1971),X1973),X1972)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_615])])]) ).

fof(i_0_726,plain,
    ! [X1916,X1917,X1918] :
      ( ~ linorder(X1916)
      | hBOOL(hAPP(X1916,bool,hAPP(X1916,fun(X1916,bool),ord_less(X1916),X1917),X1918))
      | ti(X1916,X1917) = ti(X1916,X1918)
      | hBOOL(hAPP(X1916,bool,hAPP(X1916,fun(X1916,bool),ord_less(X1916),X1918),X1917)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_616])])]) ).

fof(i_0_727,plain,
    ! [X1849,X1850,X1851,X1852,X1853,X1854] :
      ( ( ti(X1850,X1851) = ti(X1850,X1853)
        | hAPP(X1849,product_prod(X1850,X1849),hAPP(X1850,fun(X1849,product_prod(X1850,X1849)),product_Pair(X1850,X1849),X1851),X1852) != hAPP(X1849,product_prod(X1850,X1849),hAPP(X1850,fun(X1849,product_prod(X1850,X1849)),product_Pair(X1850,X1849),X1853),X1854) )
      & ( ti(X1849,X1852) = ti(X1849,X1854)
        | hAPP(X1849,product_prod(X1850,X1849),hAPP(X1850,fun(X1849,product_prod(X1850,X1849)),product_Pair(X1850,X1849),X1851),X1852) != hAPP(X1849,product_prod(X1850,X1849),hAPP(X1850,fun(X1849,product_prod(X1850,X1849)),product_Pair(X1850,X1849),X1853),X1854) )
      & ( ti(X1850,X1851) != ti(X1850,X1853)
        | ti(X1849,X1852) != ti(X1849,X1854)
        | hAPP(X1849,product_prod(X1850,X1849),hAPP(X1850,fun(X1849,product_prod(X1850,X1849)),product_Pair(X1850,X1849),X1851),X1852) = hAPP(X1849,product_prod(X1850,X1849),hAPP(X1850,fun(X1849,product_prod(X1850,X1849)),product_Pair(X1850,X1849),X1853),X1854) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_Pair__eq])])]) ).

fof(i_0_728,plain,
    ! [X1843,X1844,X1845,X1846,X1847,X1848] :
      ( ( ti(X1844,X1845) = ti(X1844,X1847)
        | hAPP(X1843,product_prod(X1844,X1843),hAPP(X1844,fun(X1843,product_prod(X1844,X1843)),product_Pair(X1844,X1843),X1845),X1846) != hAPP(X1843,product_prod(X1844,X1843),hAPP(X1844,fun(X1843,product_prod(X1844,X1843)),product_Pair(X1844,X1843),X1847),X1848) )
      & ( ti(X1843,X1846) = ti(X1843,X1848)
        | hAPP(X1843,product_prod(X1844,X1843),hAPP(X1844,fun(X1843,product_prod(X1844,X1843)),product_Pair(X1844,X1843),X1845),X1846) != hAPP(X1843,product_prod(X1844,X1843),hAPP(X1844,fun(X1843,product_prod(X1844,X1843)),product_Pair(X1844,X1843),X1847),X1848) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_Pair__inject])])]) ).

fof(i_0_729,plain,
    ! [X1968,X1969,X1970] :
      ( ~ order(X1968)
      | ~ hBOOL(hAPP(X1968,bool,hAPP(X1968,fun(X1968,bool),ord_less(X1968),X1969),X1970))
      | ti(X1968,X1969) != ti(X1968,X1970) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_67_less__imp__neq])])]) ).

fof(i_0_730,plain,
    ! [X1959,X1960,X1961] :
      ( ~ order(X1959)
      | ~ hBOOL(hAPP(X1959,bool,hAPP(X1959,fun(X1959,bool),ord_less(X1959),X1960),X1961))
      | ti(X1959,X1960) != ti(X1959,X1961) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_64_order__less__imp__not__eq])])]) ).

fof(i_0_731,plain,
    ! [X1956,X1957,X1958] :
      ( ~ order(X1956)
      | ~ hBOOL(hAPP(X1956,bool,hAPP(X1956,fun(X1956,bool),ord_less(X1956),X1957),X1958))
      | ti(X1956,X1958) != ti(X1956,X1957) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_order__less__imp__not__eq2])])]) ).

fof(i_0_732,plain,
    ! [X2287,X2288,X2289] :
      ( ( hAPP(X2287,X2288,X2289,esk35_3(X2287,X2288,X2289)) = hAPP(X2287,X2288,X2289,esk36_3(X2287,X2288,X2289))
        | hBOOL(hAPP(fun(X2287,bool),bool,hAPP(fun(X2287,X2288),fun(fun(X2287,bool),bool),inj_on(X2287,X2288),X2289),top_top(fun(X2287,bool)))) )
      & ( ti(X2287,esk35_3(X2287,X2288,X2289)) != ti(X2287,esk36_3(X2287,X2288,X2289))
        | hBOOL(hAPP(fun(X2287,bool),bool,hAPP(fun(X2287,X2288),fun(fun(X2287,bool),bool),inj_on(X2287,X2288),X2289),top_top(fun(X2287,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_152_injI])])])]) ).

fof(i_0_733,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_93_linorder__le__cases]) ).

fof(i_0_734,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_115_leI]) ).

fof(i_0_735,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X34,X33] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_116_not__leE]) ).

fof(i_0_736,plain,
    ! [X2515,X2516,X2517] :
      ( ti(fun(X2515,bool),X2516) != ti(fun(X2515,bool),X2517)
      | hBOOL(hAPP(fun(X2515,bool),bool,hAPP(fun(X2515,bool),fun(fun(X2515,bool),bool),ord_less_eq(fun(X2515,bool)),X2516),X2517)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_204_equalityD1])]) ).

fof(i_0_737,plain,
    ! [X2483,X2484,X2485] :
      ( ( hBOOL(hAPP(fun(X2483,bool),bool,hAPP(fun(X2483,bool),fun(fun(X2483,bool),bool),ord_less_eq(fun(X2483,bool)),X2484),X2485))
        | ti(fun(X2483,bool),X2484) != ti(fun(X2483,bool),X2485) )
      & ( hBOOL(hAPP(fun(X2483,bool),bool,hAPP(fun(X2483,bool),fun(fun(X2483,bool),bool),ord_less_eq(fun(X2483,bool)),X2485),X2484))
        | ti(fun(X2483,bool),X2484) != ti(fun(X2483,bool),X2485) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_617])])]) ).

fof(i_0_738,plain,
    ! [X2512,X2513,X2514] :
      ( ti(fun(X2512,bool),X2513) != ti(fun(X2512,bool),X2514)
      | hBOOL(hAPP(fun(X2512,bool),bool,hAPP(fun(X2512,bool),fun(fun(X2512,bool),bool),ord_less_eq(fun(X2512,bool)),X2514),X2513)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_203_equalityD2])]) ).

fof(i_0_739,plain,
    ! [X1749,X1750] : ti(fun(fun(X1749,bool),fun(fun(X1749,fun(X1750,bool)),fun(fun(X1749,X1750),bool))),pi(X1749,X1750)) = pi(X1749,X1750),
    inference(variable_rename,[status(thm)],[tsy_c_FuncSet_OPi_res]) ).

fof(i_0_740,plain,
    ! [X33,X34] :
      ( X33 != X34
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_223_linorder__neqE__nat]) ).

fof(i_0_741,plain,
    ! [X2336,X2337,X2338,X2339] :
      ( ( hAPP(X2336,X2336,hAPP(X2336,fun(X2336,X2336),plus_plus(X2336),X2337),X2338) != hAPP(X2336,X2336,hAPP(X2336,fun(X2336,X2336),plus_plus(X2336),X2339),X2338)
        | ti(X2336,X2337) = ti(X2336,X2339)
        | ~ cancel_semigroup_add(X2336) )
      & ( ti(X2336,X2337) != ti(X2336,X2339)
        | hAPP(X2336,X2336,hAPP(X2336,fun(X2336,X2336),plus_plus(X2336),X2337),X2338) = hAPP(X2336,X2336,hAPP(X2336,fun(X2336,X2336),plus_plus(X2336),X2339),X2338)
        | ~ cancel_semigroup_add(X2336) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_164_add__right__cancel])])])]) ).

fof(i_0_742,plain,
    ! [X2324,X2325,X2326,X2327] :
      ( ~ cancel_semigroup_add(X2324)
      | hAPP(X2324,X2324,hAPP(X2324,fun(X2324,X2324),plus_plus(X2324),X2325),X2326) != hAPP(X2324,X2324,hAPP(X2324,fun(X2324,X2324),plus_plus(X2324),X2327),X2326)
      | ti(X2324,X2325) = ti(X2324,X2327) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_161_add__right__imp__eq])])]) ).

fof(i_0_743,plain,
    ! [X2328,X2329,X2330,X2331] :
      ( ~ cancel146912293up_add(X2328)
      | hAPP(X2328,X2328,hAPP(X2328,fun(X2328,X2328),plus_plus(X2328),X2329),X2330) != hAPP(X2328,X2328,hAPP(X2328,fun(X2328,X2328),plus_plus(X2328),X2329),X2331)
      | ti(X2328,X2330) = ti(X2328,X2331) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_162_add__imp__eq])])]) ).

fof(i_0_744,plain,
    ! [X2340,X2341,X2342,X2343] :
      ( ( hAPP(X2340,X2340,hAPP(X2340,fun(X2340,X2340),plus_plus(X2340),X2341),X2342) != hAPP(X2340,X2340,hAPP(X2340,fun(X2340,X2340),plus_plus(X2340),X2341),X2343)
        | ti(X2340,X2342) = ti(X2340,X2343)
        | ~ cancel_semigroup_add(X2340) )
      & ( ti(X2340,X2342) != ti(X2340,X2343)
        | hAPP(X2340,X2340,hAPP(X2340,fun(X2340,X2340),plus_plus(X2340),X2341),X2342) = hAPP(X2340,X2340,hAPP(X2340,fun(X2340,X2340),plus_plus(X2340),X2341),X2343)
        | ~ cancel_semigroup_add(X2340) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_165_add__left__cancel])])])]) ).

fof(i_0_745,plain,
    ! [X2332,X2333,X2334,X2335] :
      ( ~ cancel_semigroup_add(X2332)
      | hAPP(X2332,X2332,hAPP(X2332,fun(X2332,X2332),plus_plus(X2332),X2333),X2334) != hAPP(X2332,X2332,hAPP(X2332,fun(X2332,X2332),plus_plus(X2332),X2333),X2335)
      | ti(X2332,X2334) = ti(X2332,X2335) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_163_add__left__imp__eq])])]) ).

fof(i_0_746,plain,
    ! [X1989,X1990,X1991,X1992] :
      ( hAPP(X1989,X1990,X1991,esk20_4(X1989,X1990,X1991,X1992)) != hAPP(X1989,X1990,X1992,esk20_4(X1989,X1990,X1991,X1992))
      | ti(fun(X1989,X1990),X1991) = ti(fun(X1989,X1990),X1992) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_ext])])]) ).

fof(i_0_747,plain,
    ! [X3428,X3429,X3430] :
      ( ~ hBOOL(hAPP(X3428,bool,hAPP(X3428,fun(X3428,bool),fequal(X3428),X3429),X3430))
      | ti(X3428,X3429) = ti(X3428,X3430) ),
    inference(variable_rename,[status(thm)],[i_0_618]) ).

fof(i_0_748,plain,
    ! [X1895,X1896] :
      ( ( ti(X1895,X1896) = top_top(X1895)
        | hBOOL(hAPP(X1895,bool,hAPP(X1895,fun(X1895,bool),ord_less(X1895),X1896),top_top(X1895)))
        | ~ top(X1895) )
      & ( ~ hBOOL(hAPP(X1895,bool,hAPP(X1895,fun(X1895,bool),ord_less(X1895),X1896),top_top(X1895)))
        | ti(X1895,X1896) != top_top(X1895)
        | ~ top(X1895) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_less__top])])])]) ).

fof(i_0_749,plain,
    ! [X2189,X2190] :
      ( ~ top(X2189)
      | ~ hBOOL(hAPP(X2189,bool,hAPP(X2189,fun(X2189,bool),ord_less_eq(X2189),top_top(X2189)),X2190))
      | ti(X2189,X2190) = top_top(X2189) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_132_top__le])])]) ).

fof(i_0_750,plain,
    ! [X2187,X2188] :
      ( ( ~ hBOOL(hAPP(X2187,bool,hAPP(X2187,fun(X2187,bool),ord_less_eq(X2187),top_top(X2187)),X2188))
        | ti(X2187,X2188) = top_top(X2187)
        | ~ top(X2187) )
      & ( ti(X2187,X2188) != top_top(X2187)
        | hBOOL(hAPP(X2187,bool,hAPP(X2187,fun(X2187,bool),ord_less_eq(X2187),top_top(X2187)),X2188))
        | ~ top(X2187) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_131_top__unique])])])]) ).

fof(i_0_751,plain,
    ! [X3] :
      ( linordered_semidom(X3)
     => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),one_one(X3)),zero_zero(X3))) ),
    inference(fof_simplification,[status(thm)],[fact_352_not__one__le__zero]) ).

fof(i_0_752,plain,
    ! [X3] :
      ( linordered_semidom(X3)
     => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),zero_zero(X3))) ),
    inference(fof_simplification,[status(thm)],[fact_354_not__one__less__zero]) ).

fof(i_0_753,plain,
    ! [X3] :
      ( top(X3)
     => ! [X21] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),top_top(X3)),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_30_not__top__less]) ).

fof(i_0_754,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X33] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X33)) ),
    inference(fof_simplification,[status(thm)],[fact_73_order__less__irrefl]) ).

fof(i_0_755,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[fact_324_not__less0]) ).

fof(i_0_756,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[fact_322_less__nat__zero__code]) ).

fof(i_0_757,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[fact_318_less__zeroE]) ).

fof(i_0_758,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X53)),
    inference(fof_simplification,[status(thm)],[fact_224_less__irrefl__nat]) ).

fof(i_0_759,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X53)),
    inference(fof_simplification,[status(thm)],[fact_221_less__not__refl]) ).

fof(i_0_760,plain,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87))
      | hBOOL(X86)
      | hBOOL(X87) ),
    inference(fof_simplification,[status(thm)],[help_fdisj_3_1_U]) ).

fof(i_0_761,plain,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87))
      | hBOOL(X86) ),
    inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).

fof(i_0_762,plain,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87))
      | hBOOL(X87) ),
    inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).

fof(i_0_763,plain,
    ! [X3431,X3432,X3433] :
      ( ti(X3431,X3432) != ti(X3431,X3433)
      | hBOOL(hAPP(X3431,bool,hAPP(X3431,fun(X3431,bool),fequal(X3431),X3432),X3433)) ),
    inference(variable_rename,[status(thm)],[help_fequal_2_1_T]) ).

fof(i_0_764,plain,
    ! [X3382,X3383,X3384] : hAPP(X3382,X3382,hAPP(X3382,fun(X3382,X3382),hAPP(bool,fun(X3382,fun(X3382,X3382)),if(X3382),fTrue),X3383),X3384) = ti(X3382,X3383),
    inference(variable_rename,[status(thm)],[help_If_1_1_T]) ).

fof(i_0_765,plain,
    ! [X3385,X3386,X3387] : hAPP(X3385,X3385,hAPP(X3385,fun(X3385,X3385),hAPP(bool,fun(X3385,fun(X3385,X3385)),if(X3385),fFalse),X3386),X3387) = ti(X3385,X3387),
    inference(variable_rename,[status(thm)],[help_If_2_1_T]) ).

fof(i_0_766,plain,
    ! [X1773,X1774] : ti(fun(fun(X1773,bool),fun(fun(X1774,bool),fun(sum_sum(X1773,X1774),bool))),sum_Plus(X1773,X1774)) = sum_Plus(X1773,X1774),
    inference(variable_rename,[status(thm)],[tsy_c_Sum__Type_OPlus_res]) ).

fof(i_0_767,plain,
    ! [X2807,X2808] :
      ( ~ hBOOL(hAPP(fun(X2807,bool),bool,finite_finite_1(X2807),top_top(fun(X2807,bool))))
      | hAPP(fun(X2807,bool),nat,finite_card(X2807),X2808) != hAPP(fun(X2807,bool),nat,finite_card(X2807),top_top(fun(X2807,bool)))
      | ti(fun(X2807,bool),X2808) = top_top(fun(X2807,bool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_298_card__eq__UNIV__imp__eq__UNIV])]) ).

fof(i_0_768,plain,
    ! [X1737,X1738,X1739] : ti(fun(fun(X1737,fun(X1738,X1739)),fun(fun(X1737,X1738),fun(X1737,X1739))),combs(X1737,X1738,X1739)) = combs(X1737,X1738,X1739),
    inference(variable_rename,[status(thm)],[tsy_c_COMBS_res]) ).

fof(i_0_769,plain,
    ! [X3003,X3004,X3005] :
      ( ( ti(X3003,X3004) != hAPP(X3003,X3003,hAPP(X3003,fun(X3003,X3003),plus_plus(X3003),X3004),X3005)
        | ti(X3003,X3005) = zero_zero(X3003)
        | ~ semiri456707255roduct(X3003) )
      & ( ti(X3003,X3005) != zero_zero(X3003)
        | ti(X3003,X3004) = hAPP(X3003,X3003,hAPP(X3003,fun(X3003,X3003),plus_plus(X3003),X3004),X3005)
        | ~ semiri456707255roduct(X3003) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_373_add__0__iff])])])]) ).

fof(i_0_770,plain,
    ! [X1766,X1767,X1768] : ti(fun(fun(X1766,fun(X1767,X1768)),fun(product_prod(X1766,X1767),X1768)),product_prod_rec(X1766,X1767,X1768)) = product_prod_rec(X1766,X1767,X1768),
    inference(variable_rename,[status(thm)],[tsy_c_Product__Type_Oprod_Oprod__rec_res]) ).

fof(i_0_771,plain,
    ! [X1731,X1732,X1733] : ti(fun(fun(X1731,fun(X1732,X1733)),fun(X1732,fun(X1731,X1733))),combc(X1731,X1732,X1733)) = combc(X1731,X1732,X1733),
    inference(variable_rename,[status(thm)],[tsy_c_COMBC_res]) ).

fof(i_0_772,plain,
    ! [X1728,X1729,X1730] : ti(fun(fun(X1728,X1729),fun(fun(X1730,X1728),fun(X1730,X1729))),combb(X1728,X1729,X1730)) = combb(X1728,X1729,X1730),
    inference(variable_rename,[status(thm)],[tsy_c_COMBB_res]) ).

fof(i_0_773,plain,
    ! [X1757,X1758] : ti(fun(fun(X1757,bool),fun(fun(X1757,X1758),fun(X1758,X1757))),hilbert_inv_into(X1757,X1758)) = hilbert_inv_into(X1757,X1758),
    inference(variable_rename,[status(thm)],[tsy_c_Hilbert__Choice_Oinv__into_res]) ).

fof(i_0_774,plain,
    ! [X1745,X1746] : ti(fun(fun(product_prod(X1745,X1746),bool),fun(X1745,fun(X1746,bool))),in_rel(X1745,X1746)) = in_rel(X1745,X1746),
    inference(variable_rename,[status(thm)],[tsy_c_FunDef_Oin__rel_res]) ).

fof(i_0_775,plain,
    ! [X87,X86] :
      ( ~ hBOOL(X86)
      | ~ hBOOL(X87)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87)) ),
    inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).

fof(i_0_776,plain,
    ! [X87,X86] :
      ( ~ hBOOL(X86)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87)) ),
    inference(fof_simplification,[status(thm)],[help_fdisj_1_1_U]) ).

fof(i_0_777,plain,
    ! [X86,X87] :
      ( ~ hBOOL(X87)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87)) ),
    inference(fof_simplification,[status(thm)],[help_fdisj_2_1_U]) ).

fof(i_0_778,plain,
    ! [X1771,X1772] : ti(fun(fun(X1771,X1772),fun(fun(X1771,bool),fun(X1772,bool))),image(X1771,X1772)) = image(X1771,X1772),
    inference(variable_rename,[status(thm)],[tsy_c_Set_Oimage_res]) ).

fof(i_0_779,plain,
    ! [X2999,X3000] :
      ( ( hAPP(X2999,X2999,hAPP(X2999,fun(X2999,X2999),plus_plus(X2999),X3000),X3000) != zero_zero(X2999)
        | ti(X2999,X3000) = zero_zero(X2999)
        | ~ linord219039673up_add(X2999) )
      & ( ti(X2999,X3000) != zero_zero(X2999)
        | hAPP(X2999,X2999,hAPP(X2999,fun(X2999,X2999),plus_plus(X2999),X3000),X3000) = zero_zero(X2999)
        | ~ linord219039673up_add(X2999) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_371_double__eq__0__iff])])])]) ).

fof(i_0_780,plain,
    ! [X2910,X2911] :
      ( ( zero_zero(X2910) != hAPP(X2910,X2910,hAPP(X2910,fun(X2910,X2910),plus_plus(X2910),X2911),X2911)
        | ti(X2910,X2911) = zero_zero(X2910)
        | ~ linord219039673up_add(X2910) )
      & ( ti(X2910,X2911) != zero_zero(X2910)
        | zero_zero(X2910) = hAPP(X2910,X2910,hAPP(X2910,fun(X2910,X2910),plus_plus(X2910),X2911),X2911)
        | ~ linord219039673up_add(X2910) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_336_double__zero__sym])])])]) ).

fof(i_0_781,plain,
    ! [X3301,X3302] : hAPP(fun(X3301,bool),fun(X3301,bool),hAPP(fun(X3301,X3301),fun(fun(X3301,bool),fun(X3301,bool)),image(X3301,X3301),combi(X3301)),X3302) = ti(fun(X3301,bool),X3302),
    inference(variable_rename,[status(thm)],[fact_484_image__ident]) ).

fof(i_0_782,plain,
    ! [X1776,X1777,X1778,X1779] : hAPP(X1776,X1777,ti(fun(X1776,X1777),X1778),X1779) = hAPP(X1776,X1777,X1778,X1779),
    inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg1]) ).

fof(i_0_783,plain,
    ! [X1747,X1748] : ti(fun(fun(X1747,X1748),fun(fun(X1747,bool),bool)),inj_on(X1747,X1748)) = inj_on(X1747,X1748),
    inference(variable_rename,[status(thm)],[tsy_c_Fun_Oinj__on_res]) ).

fof(i_0_784,plain,
    ! [X3405,X3406,X3407,X3408] : hAPP(X3405,X3406,hAPP(X3406,fun(X3405,X3406),combk(X3406,X3405),X3407),X3408) = ti(X3406,X3407),
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_U]) ).

fof(i_0_785,plain,
    ! [X3136,X3137] :
      ( ~ comm_semiring_1(X3136)
      | hAPP(X3136,X3136,hAPP(X3136,fun(X3136,X3136),plus_plus(X3136),zero_zero(X3136)),X3137) = ti(X3136,X3137) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])]) ).

fof(i_0_786,plain,
    ! [X2912,X2913] :
      ( ~ comm_monoid_add(X2912)
      | hAPP(X2912,X2912,hAPP(X2912,fun(X2912,X2912),plus_plus(X2912),zero_zero(X2912)),X2913) = ti(X2912,X2913) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_337_add__0])])]) ).

fof(i_0_787,plain,
    ! [X2914,X2915] :
      ( ~ monoid_add(X2914)
      | hAPP(X2914,X2914,hAPP(X2914,fun(X2914,X2914),plus_plus(X2914),zero_zero(X2914)),X2915) = ti(X2914,X2915) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_338_add__0__left])])]) ).

fof(i_0_788,plain,
    ! [X3138,X3139] :
      ( ~ comm_semiring_1(X3138)
      | hAPP(X3138,X3138,hAPP(X3138,fun(X3138,X3138),plus_plus(X3138),X3139),zero_zero(X3138)) = ti(X3138,X3139) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])]) ).

fof(i_0_789,plain,
    ! [X2906,X2907] :
      ( ~ comm_monoid_add(X2906)
      | hAPP(X2906,X2906,hAPP(X2906,fun(X2906,X2906),plus_plus(X2906),X2907),zero_zero(X2906)) = ti(X2906,X2907) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_334_add_Ocomm__neutral])])]) ).

fof(i_0_790,plain,
    ! [X2908,X2909] :
      ( ~ monoid_add(X2908)
      | hAPP(X2908,X2908,hAPP(X2908,fun(X2908,X2908),plus_plus(X2908),X2909),zero_zero(X2908)) = ti(X2908,X2909) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_335_add__0__right])])]) ).

fof(i_0_791,plain,
    ! [X1764,X1765] : ti(fun(X1764,fun(X1765,product_prod(X1764,X1765))),product_Pair(X1764,X1765)) = product_Pair(X1764,X1765),
    inference(variable_rename,[status(thm)],[tsy_c_Product__Type_OPair_res]) ).

fof(i_0_792,plain,
    ! [X3380,X3381] : ti(X3380,ti(X3380,X3381)) = ti(X3380,X3381),
    inference(variable_rename,[status(thm)],[help_ti_idem]) ).

fof(i_0_793,plain,
    ! [X1780,X1781,X1782,X1783] : hAPP(X1780,X1781,X1782,ti(X1780,X1783)) = hAPP(X1780,X1781,X1782,X1783),
    inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg2]) ).

fof(i_0_794,plain,
    ! [X1784,X1785,X1786,X1787] : ti(X1784,hAPP(X1785,X1784,X1786,X1787)) = hAPP(X1785,X1784,X1786,X1787),
    inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).

fof(i_0_795,plain,
    ! [X1759] : ti(fun(bool,fun(X1759,fun(X1759,X1759))),if(X1759)) = if(X1759),
    inference(variable_rename,[status(thm)],[tsy_c_If_res]) ).

fof(i_0_796,plain,
    ! [X1769] :
      ( ~ linorder(X1769)
      | ti(fun(X1769,fun(X1769,fun(X1769,bool))),ord_atLeastLessThan(X1769)) = ord_atLeastLessThan(X1769) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OatLeastLessThan_res])]) ).

fof(i_0_797,plain,
    ! [X1789] : ti(fun(X1789,fun(fun(X1789,bool),bool)),member(X1789)) = member(X1789),
    inference(variable_rename,[status(thm)],[tsy_c_member_res]) ).

fof(i_0_798,plain,
    ! [X3,X39] :
      ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ),
    inference(fof_simplification,[status(thm)],[fact_356_card__infinite]) ).

fof(i_0_799,hypothesis,
    ! [X1788] :
      ( ( ~ hBOOL(ti(bool,X1788))
        | hBOOL(X1788) )
      & ( ~ hBOOL(X1788)
        | hBOOL(ti(bool,X1788)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1])]) ).

fof(i_0_800,plain,
    ! [X86] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X86))
      | ~ hBOOL(X86) ),
    inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).

fof(i_0_801,plain,
    ! [X1770] : ti(fun(fun(X1770,bool),fun(X1770,bool)),collect(X1770)) = collect(X1770),
    inference(variable_rename,[status(thm)],[tsy_c_Set_OCollect_res]) ).

fof(i_0_802,plain,
    ! [X1997,X1998] : hAPP(fun(X1997,bool),fun(X1997,bool),collect(X1997),X1998) = ti(fun(X1997,bool),X1998),
    inference(variable_rename,[status(thm)],[fact_77_Collect__def]) ).

fof(i_0_803,plain,
    ! [X1735,X1736] : ti(fun(X1735,fun(X1736,X1735)),combk(X1735,X1736)) = combk(X1735,X1736),
    inference(variable_rename,[status(thm)],[tsy_c_COMBK_res]) ).

fof(i_0_804,plain,
    ! [X1754] :
      ( ~ cancel_semigroup_add(X1754)
      | ti(fun(X1754,fun(X1754,X1754)),plus_plus(X1754)) = plus_plus(X1754) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_2_res])]) ).

fof(i_0_805,plain,
    ! [X1753] :
      ( ~ ab_semigroup_add(X1753)
      | ti(fun(X1753,fun(X1753,X1753)),plus_plus(X1753)) = plus_plus(X1753) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_1_res])]) ).

fof(i_0_806,plain,
    ! [X1752] :
      ( ~ monoid_add(X1752)
      | ti(fun(X1752,fun(X1752,X1752)),plus_plus(X1752)) = plus_plus(X1752) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_0_res])]) ).

fof(i_0_807,plain,
    ! [X1762] :
      ( ~ ord(X1762)
      | ti(fun(X1762,fun(X1762,bool)),ord_less_eq(X1762)) = ord_less_eq(X1762) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res])]) ).

fof(i_0_808,plain,
    ! [X1761] :
      ( ~ ord(X1761)
      | ti(fun(X1761,fun(X1761,bool)),ord_less(X1761)) = ord_less(X1761) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless_res])]) ).

fof(i_0_809,plain,
    ! [X1775] : ti(fun(X1775,fun(X1775,bool)),fequal(X1775)) = fequal(X1775),
    inference(variable_rename,[status(thm)],[tsy_c_fequal_res]) ).

fof(i_0_810,plain,
    ! [X1740] : ti(fun(fun(X1740,bool),nat),finite_card(X1740)) = finite_card(X1740),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ocard_res]) ).

fof(i_0_811,plain,
    ! [X1741] : ti(fun(fun(X1741,bool),bool),finite_finite_1(X1741)) = finite_finite_1(X1741),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofinite_res]) ).

fof(i_0_812,plain,
    ! [X3415] :
      ( ti(bool,X3415) = fTrue
      | ti(bool,X3415) = fFalse ),
    inference(variable_rename,[status(thm)],[help_fTrue_1_1_T]) ).

fof(i_0_813,plain,
    ! [X3388] :
      ( ti(bool,X3388) = fTrue
      | ti(bool,X3388) = fFalse ),
    inference(variable_rename,[status(thm)],[help_If_3_1_T]) ).

fof(i_0_814,plain,
    ! [X1734] : ti(fun(X1734,X1734),combi(X1734)) = combi(X1734),
    inference(variable_rename,[status(thm)],[tsy_c_COMBI_res]) ).

fof(i_0_815,plain,
    ! [X1760] :
      ( ~ ring_1(X1760)
      | ti(fun(X1760,bool),ring_1_Ints(X1760)) = ring_1_Ints(X1760) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Int_Oring__1__class_OInts_res])]) ).

fof(i_0_816,plain,
    ! [X1763] :
      ( ~ top(X1763)
      | ti(X1763,top_top(X1763)) = top_top(X1763) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Otop__class_Otop_res])]) ).

fof(i_0_817,plain,
    ! [X1755] :
      ( ~ zero(X1755)
      | ti(X1755,zero_zero(X1755)) = zero_zero(X1755) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ozero__class_Ozero_res])]) ).

fof(i_0_818,plain,
    ! [X1751] :
      ( ~ one(X1751)
      | ti(X1751,one_one(X1751)) = one_one(X1751) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_res])]) ).

fof(i_0_819,plain,
    ! [X1756] : ti(X1756,undefined(X1756)) = undefined(X1756),
    inference(variable_rename,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).

fof(i_0_820,plain,
    ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) )
    & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_81__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_821,plain,
    ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) )
    & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_33__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_822,plain,
    ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) )
    & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ) ),
    inference(fof_nnf,[status(thm)],[fact_14_PW]) ).

fof(i_0_823,plain,
    ! [X2054] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2054),esk28_0))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X2054))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),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_619])])])]) ).

fof(i_0_824,plain,
    ! [X2052] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk27_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2052),esk27_0))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X2052))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),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_91__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_])])])]) ).

fof(i_0_825,plain,
    ! [X1901] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1901),n))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1901))),lab)),lba)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_45_n_I2_J])]) ).

fof(i_0_826,plain,
    ! [X1897] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1897))),lab)),lba)),arrow_1111136790e_Prof)),
    inference(variable_rename,[status(thm)],[fact_41_PiProf]) ).

fof(i_0_827,plain,
    ! [X2310,X2311,X2312,X2313] :
      ( ( ~ hBOOL(hAPP(fun(X2310,fun(X2311,bool)),bool,hAPP(fun(X2310,fun(X2311,bool)),fun(fun(X2310,fun(X2311,bool)),bool),ord_less_eq(fun(X2310,fun(X2311,bool))),hAPP(fun(product_prod(X2310,X2311),bool),fun(X2310,fun(X2311,bool)),hAPP(fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),fun(fun(product_prod(X2310,X2311),bool),fun(X2310,fun(X2311,bool))),combc(X2310,fun(product_prod(X2310,X2311),bool),fun(X2311,bool)),hAPP(fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),hAPP(fun(fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),fun(fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool)))),combb(fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool)),X2310),combc(X2311,fun(product_prod(X2310,X2311),bool),bool)),hAPP(fun(X2310,fun(X2311,product_prod(X2310,X2311))),fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),hAPP(fun(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(fun(X2310,fun(X2311,product_prod(X2310,X2311))),fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)))),combb(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),X2310),hAPP(fun(product_prod(X2310,X2311),fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),combb(product_prod(X2310,X2311),fun(fun(product_prod(X2310,X2311),bool),bool),X2311),member(product_prod(X2310,X2311)))),product_Pair(X2310,X2311)))),X2312)),hAPP(fun(product_prod(X2310,X2311),bool),fun(X2310,fun(X2311,bool)),hAPP(fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),fun(fun(product_prod(X2310,X2311),bool),fun(X2310,fun(X2311,bool))),combc(X2310,fun(product_prod(X2310,X2311),bool),fun(X2311,bool)),hAPP(fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),hAPP(fun(fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),fun(fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool)))),combb(fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool)),X2310),combc(X2311,fun(product_prod(X2310,X2311),bool),bool)),hAPP(fun(X2310,fun(X2311,product_prod(X2310,X2311))),fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),hAPP(fun(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(fun(X2310,fun(X2311,product_prod(X2310,X2311))),fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)))),combb(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),X2310),hAPP(fun(product_prod(X2310,X2311),fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),combb(product_prod(X2310,X2311),fun(fun(product_prod(X2310,X2311),bool),bool),X2311),member(product_prod(X2310,X2311)))),product_Pair(X2310,X2311)))),X2313)))
        | hBOOL(hAPP(fun(product_prod(X2310,X2311),bool),bool,hAPP(fun(product_prod(X2310,X2311),bool),fun(fun(product_prod(X2310,X2311),bool),bool),ord_less_eq(fun(product_prod(X2310,X2311),bool)),X2312),X2313)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X2310,X2311),bool),bool,hAPP(fun(product_prod(X2310,X2311),bool),fun(fun(product_prod(X2310,X2311),bool),bool),ord_less_eq(fun(product_prod(X2310,X2311),bool)),X2312),X2313))
        | hBOOL(hAPP(fun(X2310,fun(X2311,bool)),bool,hAPP(fun(X2310,fun(X2311,bool)),fun(fun(X2310,fun(X2311,bool)),bool),ord_less_eq(fun(X2310,fun(X2311,bool))),hAPP(fun(product_prod(X2310,X2311),bool),fun(X2310,fun(X2311,bool)),hAPP(fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),fun(fun(product_prod(X2310,X2311),bool),fun(X2310,fun(X2311,bool))),combc(X2310,fun(product_prod(X2310,X2311),bool),fun(X2311,bool)),hAPP(fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),hAPP(fun(fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),fun(fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool)))),combb(fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool)),X2310),combc(X2311,fun(product_prod(X2310,X2311),bool),bool)),hAPP(fun(X2310,fun(X2311,product_prod(X2310,X2311))),fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),hAPP(fun(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(fun(X2310,fun(X2311,product_prod(X2310,X2311))),fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)))),combb(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),X2310),hAPP(fun(product_prod(X2310,X2311),fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),combb(product_prod(X2310,X2311),fun(fun(product_prod(X2310,X2311),bool),bool),X2311),member(product_prod(X2310,X2311)))),product_Pair(X2310,X2311)))),X2312)),hAPP(fun(product_prod(X2310,X2311),bool),fun(X2310,fun(X2311,bool)),hAPP(fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),fun(fun(product_prod(X2310,X2311),bool),fun(X2310,fun(X2311,bool))),combc(X2310,fun(product_prod(X2310,X2311),bool),fun(X2311,bool)),hAPP(fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),hAPP(fun(fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool))),fun(fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(X2310,fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool)))),combb(fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(product_prod(X2310,X2311),bool),fun(X2311,bool)),X2310),combc(X2311,fun(product_prod(X2310,X2311),bool),bool)),hAPP(fun(X2310,fun(X2311,product_prod(X2310,X2311))),fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),hAPP(fun(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),fun(fun(X2310,fun(X2311,product_prod(X2310,X2311))),fun(X2310,fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)))),combb(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool)),X2310),hAPP(fun(product_prod(X2310,X2311),fun(fun(product_prod(X2310,X2311),bool),bool)),fun(fun(X2311,product_prod(X2310,X2311)),fun(X2311,fun(fun(product_prod(X2310,X2311),bool),bool))),combb(product_prod(X2310,X2311),fun(fun(product_prod(X2310,X2311),bool),bool),X2311),member(product_prod(X2310,X2311)))),product_Pair(X2310,X2311)))),X2313))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_157_pred__subset__eq2])]) ).

fof(i_0_828,plain,
    ! [X3130,X3131] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X3131))
      | hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X3131))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X3130))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X3131))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X3130))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_433_card__less__Suc])]) ).

fof(i_0_829,plain,
    ! [X3134,X3135] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X3135))
      | hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X3135))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X3134)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X3135))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X3134))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_620])]) ).

fof(i_0_830,plain,
    ! [X2421,X2422,X2423,X2424,X2425,X2426] :
      ( ( hBOOL(hAPP(X2421,bool,hAPP(X2421,fun(X2421,bool),ord_less_eq(X2421),esk43_6(X2421,X2422,X2423,X2424,X2425,X2426)),esk42_6(X2421,X2422,X2423,X2424,X2425,X2426)))
        | hBOOL(hAPP(X2422,bool,hAPP(X2422,fun(X2422,bool),ord_less(X2422),hAPP(X2421,X2422,X2424,X2423)),X2426))
        | ~ hBOOL(hAPP(X2421,bool,hAPP(X2421,fun(X2421,bool),ord_less_eq(X2421),X2423),X2425))
        | ~ hBOOL(hAPP(X2422,bool,hAPP(X2422,fun(X2422,bool),ord_less(X2422),hAPP(X2421,X2422,X2424,X2425)),X2426))
        | ~ order(X2422)
        | ~ order(X2421) )
      & ( ~ hBOOL(hAPP(X2422,bool,hAPP(X2422,fun(X2422,bool),ord_less_eq(X2422),hAPP(X2421,X2422,X2424,esk43_6(X2421,X2422,X2423,X2424,X2425,X2426))),hAPP(X2421,X2422,X2424,esk42_6(X2421,X2422,X2423,X2424,X2425,X2426))))
        | hBOOL(hAPP(X2422,bool,hAPP(X2422,fun(X2422,bool),ord_less(X2422),hAPP(X2421,X2422,X2424,X2423)),X2426))
        | ~ hBOOL(hAPP(X2421,bool,hAPP(X2421,fun(X2421,bool),ord_less_eq(X2421),X2423),X2425))
        | ~ hBOOL(hAPP(X2422,bool,hAPP(X2422,fun(X2422,bool),ord_less(X2422),hAPP(X2421,X2422,X2424,X2425)),X2426))
        | ~ order(X2422)
        | ~ order(X2421) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_184_xt4])])])])]) ).

fof(i_0_831,plain,
    ! [X2413,X2414,X2415,X2416,X2417,X2418] :
      ( ( hBOOL(hAPP(X2413,bool,hAPP(X2413,fun(X2413,bool),ord_less(X2413),esk41_6(X2413,X2414,X2415,X2416,X2417,X2418)),esk40_6(X2413,X2414,X2415,X2416,X2417,X2418)))
        | hBOOL(hAPP(X2414,bool,hAPP(X2414,fun(X2414,bool),ord_less(X2414),hAPP(X2413,X2414,X2416,X2415)),X2418))
        | ~ hBOOL(hAPP(X2413,bool,hAPP(X2413,fun(X2413,bool),ord_less(X2413),X2415),X2417))
        | ~ hBOOL(hAPP(X2414,bool,hAPP(X2414,fun(X2414,bool),ord_less_eq(X2414),hAPP(X2413,X2414,X2416,X2417)),X2418))
        | ~ order(X2414)
        | ~ ord(X2413) )
      & ( ~ hBOOL(hAPP(X2414,bool,hAPP(X2414,fun(X2414,bool),ord_less(X2414),hAPP(X2413,X2414,X2416,esk41_6(X2413,X2414,X2415,X2416,X2417,X2418))),hAPP(X2413,X2414,X2416,esk40_6(X2413,X2414,X2415,X2416,X2417,X2418))))
        | hBOOL(hAPP(X2414,bool,hAPP(X2414,fun(X2414,bool),ord_less(X2414),hAPP(X2413,X2414,X2416,X2415)),X2418))
        | ~ hBOOL(hAPP(X2413,bool,hAPP(X2413,fun(X2413,bool),ord_less(X2413),X2415),X2417))
        | ~ hBOOL(hAPP(X2414,bool,hAPP(X2414,fun(X2414,bool),ord_less_eq(X2414),hAPP(X2413,X2414,X2416,X2417)),X2418))
        | ~ order(X2414)
        | ~ ord(X2413) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_183_xt6])])])])]) ).

fof(i_0_832,plain,
    ! [X2445,X2446,X2447,X2448,X2449,X2450] :
      ( ( hBOOL(hAPP(X2445,bool,hAPP(X2445,fun(X2445,bool),ord_less_eq(X2445),esk48_6(X2445,X2446,X2447,X2448,X2449,X2450)),esk49_6(X2445,X2446,X2447,X2448,X2449,X2450)))
        | hBOOL(hAPP(X2446,bool,hAPP(X2446,fun(X2446,bool),ord_less(X2446),hAPP(X2445,X2446,X2447,X2449)),X2448))
        | ~ hBOOL(hAPP(X2446,bool,hAPP(X2446,fun(X2446,bool),ord_less(X2446),hAPP(X2445,X2446,X2447,X2450)),X2448))
        | ~ hBOOL(hAPP(X2445,bool,hAPP(X2445,fun(X2445,bool),ord_less_eq(X2445),X2449),X2450))
        | ~ order(X2446)
        | ~ order(X2445) )
      & ( ~ hBOOL(hAPP(X2446,bool,hAPP(X2446,fun(X2446,bool),ord_less_eq(X2446),hAPP(X2445,X2446,X2447,esk48_6(X2445,X2446,X2447,X2448,X2449,X2450))),hAPP(X2445,X2446,X2447,esk49_6(X2445,X2446,X2447,X2448,X2449,X2450))))
        | hBOOL(hAPP(X2446,bool,hAPP(X2446,fun(X2446,bool),ord_less(X2446),hAPP(X2445,X2446,X2447,X2449)),X2448))
        | ~ hBOOL(hAPP(X2446,bool,hAPP(X2446,fun(X2446,bool),ord_less(X2446),hAPP(X2445,X2446,X2447,X2450)),X2448))
        | ~ hBOOL(hAPP(X2445,bool,hAPP(X2445,fun(X2445,bool),ord_less_eq(X2445),X2449),X2450))
        | ~ order(X2446)
        | ~ order(X2445) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_187_order__le__less__subst2])])])])]) ).

fof(i_0_833,plain,
    ! [X2570,X2571,X2572,X2573,X2574,X2575] :
      ( ( hBOOL(hAPP(X2570,bool,hAPP(X2570,fun(X2570,bool),ord_less(X2570),esk58_6(X2570,X2571,X2572,X2573,X2574,X2575)),esk59_6(X2570,X2571,X2572,X2573,X2574,X2575)))
        | hBOOL(hAPP(X2571,bool,hAPP(X2571,fun(X2571,bool),ord_less(X2571),hAPP(X2570,X2571,X2572,X2574)),X2573))
        | ~ hBOOL(hAPP(X2571,bool,hAPP(X2571,fun(X2571,bool),ord_less_eq(X2571),hAPP(X2570,X2571,X2572,X2575)),X2573))
        | ~ hBOOL(hAPP(X2570,bool,hAPP(X2570,fun(X2570,bool),ord_less(X2570),X2574),X2575))
        | ~ order(X2571)
        | ~ order(X2570) )
      & ( ~ hBOOL(hAPP(X2571,bool,hAPP(X2571,fun(X2571,bool),ord_less(X2571),hAPP(X2570,X2571,X2572,esk58_6(X2570,X2571,X2572,X2573,X2574,X2575))),hAPP(X2570,X2571,X2572,esk59_6(X2570,X2571,X2572,X2573,X2574,X2575))))
        | hBOOL(hAPP(X2571,bool,hAPP(X2571,fun(X2571,bool),ord_less(X2571),hAPP(X2570,X2571,X2572,X2574)),X2573))
        | ~ hBOOL(hAPP(X2571,bool,hAPP(X2571,fun(X2571,bool),ord_less_eq(X2571),hAPP(X2570,X2571,X2572,X2575)),X2573))
        | ~ hBOOL(hAPP(X2570,bool,hAPP(X2570,fun(X2570,bool),ord_less(X2570),X2574),X2575))
        | ~ order(X2571)
        | ~ order(X2570) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_216_order__less__le__subst2])])])])]) ).

fof(i_0_834,plain,
    ! [X2554,X2555,X2556,X2557,X2558,X2559] :
      ( ( hBOOL(hAPP(X2555,bool,hAPP(X2555,fun(X2555,bool),ord_less_eq(X2555),esk57_6(X2554,X2555,X2556,X2557,X2558,X2559)),esk56_6(X2554,X2555,X2556,X2557,X2558,X2559)))
        | hBOOL(hAPP(X2554,bool,hAPP(X2554,fun(X2554,bool),ord_less(X2554),X2556),hAPP(X2555,X2554,X2557,X2559)))
        | ~ hBOOL(hAPP(X2554,bool,hAPP(X2554,fun(X2554,bool),ord_less(X2554),X2556),hAPP(X2555,X2554,X2557,X2558)))
        | ~ hBOOL(hAPP(X2555,bool,hAPP(X2555,fun(X2555,bool),ord_less_eq(X2555),X2558),X2559))
        | ~ order(X2555)
        | ~ order(X2554) )
      & ( ~ hBOOL(hAPP(X2554,bool,hAPP(X2554,fun(X2554,bool),ord_less_eq(X2554),hAPP(X2555,X2554,X2557,esk57_6(X2554,X2555,X2556,X2557,X2558,X2559))),hAPP(X2555,X2554,X2557,esk56_6(X2554,X2555,X2556,X2557,X2558,X2559))))
        | hBOOL(hAPP(X2554,bool,hAPP(X2554,fun(X2554,bool),ord_less(X2554),X2556),hAPP(X2555,X2554,X2557,X2559)))
        | ~ hBOOL(hAPP(X2554,bool,hAPP(X2554,fun(X2554,bool),ord_less(X2554),X2556),hAPP(X2555,X2554,X2557,X2558)))
        | ~ hBOOL(hAPP(X2555,bool,hAPP(X2555,fun(X2555,bool),ord_less_eq(X2555),X2558),X2559))
        | ~ order(X2555)
        | ~ order(X2554) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_213_xt7])])])])]) ).

fof(i_0_835,plain,
    ! [X2546,X2547,X2548,X2549,X2550,X2551] :
      ( ( hBOOL(hAPP(X2547,bool,hAPP(X2547,fun(X2547,bool),ord_less(X2547),esk55_6(X2546,X2547,X2548,X2549,X2550,X2551)),esk54_6(X2546,X2547,X2548,X2549,X2550,X2551)))
        | hBOOL(hAPP(X2546,bool,hAPP(X2546,fun(X2546,bool),ord_less(X2546),X2548),hAPP(X2547,X2546,X2549,X2551)))
        | ~ hBOOL(hAPP(X2546,bool,hAPP(X2546,fun(X2546,bool),ord_less_eq(X2546),X2548),hAPP(X2547,X2546,X2549,X2550)))
        | ~ hBOOL(hAPP(X2547,bool,hAPP(X2547,fun(X2547,bool),ord_less(X2547),X2550),X2551))
        | ~ order(X2547)
        | ~ order(X2546) )
      & ( ~ hBOOL(hAPP(X2546,bool,hAPP(X2546,fun(X2546,bool),ord_less(X2546),hAPP(X2547,X2546,X2549,esk55_6(X2546,X2547,X2548,X2549,X2550,X2551))),hAPP(X2547,X2546,X2549,esk54_6(X2546,X2547,X2548,X2549,X2550,X2551))))
        | hBOOL(hAPP(X2546,bool,hAPP(X2546,fun(X2546,bool),ord_less(X2546),X2548),hAPP(X2547,X2546,X2549,X2551)))
        | ~ hBOOL(hAPP(X2546,bool,hAPP(X2546,fun(X2546,bool),ord_less_eq(X2546),X2548),hAPP(X2547,X2546,X2549,X2550)))
        | ~ hBOOL(hAPP(X2547,bool,hAPP(X2547,fun(X2547,bool),ord_less(X2547),X2550),X2551))
        | ~ order(X2547)
        | ~ order(X2546) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_212_xt5])])])])]) ).

fof(i_0_836,plain,
    ! [X2437,X2438,X2439,X2440,X2441,X2442] :
      ( ( hBOOL(hAPP(X2438,bool,hAPP(X2438,fun(X2438,bool),ord_less_eq(X2438),esk46_6(X2437,X2438,X2439,X2440,X2441,X2442)),esk47_6(X2437,X2438,X2439,X2440,X2441,X2442)))
        | hBOOL(hAPP(X2437,bool,hAPP(X2437,fun(X2437,bool),ord_less(X2437),X2440),hAPP(X2438,X2437,X2441,X2439)))
        | ~ hBOOL(hAPP(X2438,bool,hAPP(X2438,fun(X2438,bool),ord_less_eq(X2438),X2442),X2439))
        | ~ hBOOL(hAPP(X2437,bool,hAPP(X2437,fun(X2437,bool),ord_less(X2437),X2440),hAPP(X2438,X2437,X2441,X2442)))
        | ~ order(X2438)
        | ~ order(X2437) )
      & ( ~ hBOOL(hAPP(X2437,bool,hAPP(X2437,fun(X2437,bool),ord_less_eq(X2437),hAPP(X2438,X2437,X2441,esk46_6(X2437,X2438,X2439,X2440,X2441,X2442))),hAPP(X2438,X2437,X2441,esk47_6(X2437,X2438,X2439,X2440,X2441,X2442))))
        | hBOOL(hAPP(X2437,bool,hAPP(X2437,fun(X2437,bool),ord_less(X2437),X2440),hAPP(X2438,X2437,X2441,X2439)))
        | ~ hBOOL(hAPP(X2438,bool,hAPP(X2438,fun(X2438,bool),ord_less_eq(X2438),X2442),X2439))
        | ~ hBOOL(hAPP(X2437,bool,hAPP(X2437,fun(X2437,bool),ord_less(X2437),X2440),hAPP(X2438,X2437,X2441,X2442)))
        | ~ order(X2438)
        | ~ order(X2437) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_186_order__less__le__subst1])])])])]) ).

fof(i_0_837,plain,
    ! [X2429,X2430,X2431,X2432,X2433,X2434] :
      ( ( hBOOL(hAPP(X2430,bool,hAPP(X2430,fun(X2430,bool),ord_less(X2430),esk44_6(X2429,X2430,X2431,X2432,X2433,X2434)),esk45_6(X2429,X2430,X2431,X2432,X2433,X2434)))
        | hBOOL(hAPP(X2429,bool,hAPP(X2429,fun(X2429,bool),ord_less(X2429),X2432),hAPP(X2430,X2429,X2433,X2431)))
        | ~ hBOOL(hAPP(X2430,bool,hAPP(X2430,fun(X2430,bool),ord_less(X2430),X2434),X2431))
        | ~ hBOOL(hAPP(X2429,bool,hAPP(X2429,fun(X2429,bool),ord_less_eq(X2429),X2432),hAPP(X2430,X2429,X2433,X2434)))
        | ~ order(X2430)
        | ~ order(X2429) )
      & ( ~ hBOOL(hAPP(X2429,bool,hAPP(X2429,fun(X2429,bool),ord_less(X2429),hAPP(X2430,X2429,X2433,esk44_6(X2429,X2430,X2431,X2432,X2433,X2434))),hAPP(X2430,X2429,X2433,esk45_6(X2429,X2430,X2431,X2432,X2433,X2434))))
        | hBOOL(hAPP(X2429,bool,hAPP(X2429,fun(X2429,bool),ord_less(X2429),X2432),hAPP(X2430,X2429,X2433,X2431)))
        | ~ hBOOL(hAPP(X2430,bool,hAPP(X2430,fun(X2430,bool),ord_less(X2430),X2434),X2431))
        | ~ hBOOL(hAPP(X2429,bool,hAPP(X2429,fun(X2429,bool),ord_less_eq(X2429),X2432),hAPP(X2430,X2429,X2433,X2434)))
        | ~ order(X2430)
        | ~ order(X2429) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_185_order__le__less__subst1])])])])]) ).

cnf(i_0_838,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_621]) ).

cnf(i_0_839,plain,
    hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_622]) ).

cnf(i_0_840,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_621]) ).

cnf(i_0_841,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X6)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X6)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X6)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X6)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_623]) ).

cnf(i_0_842,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_624]) ).

cnf(i_0_843,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_624]) ).

cnf(i_0_844,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_621]) ).

cnf(i_0_845,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_621]) ).

cnf(i_0_846,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X6)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X6)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X6)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X6)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_623]) ).

cnf(i_0_847,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_624]) ).

cnf(i_0_848,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_624]) ).

fof(i_0_849,plain,
    ! [X3132,X3133] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X3133))
      | hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X3133))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X3132))))) != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_434_card__less])]) ).

fof(i_0_850,plain,
    ! [X2018] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X2018) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X2018) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X2018)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X2018)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_625])])]) ).

fof(i_0_851,plain,
    ! [X1830] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1830) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1830) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1830) != n
        | hAPP(arrow_660593299e_indi,nat,h,X1830) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X1830) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1830) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1830)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1830) != n
        | hAPP(arrow_660593299e_indi,nat,h,X1830) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X1830) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X1830) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1830))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_626])])]) ).

fof(i_0_852,plain,
    ! [X1855,X1856,X1857,X1858,X1859,X1861,X1866,X1867] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1855,X1856)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1855,X1857)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1856,esk9_5(X1855,X1856,X1857,X1858,X1859))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1857,esk9_5(X1855,X1856,X1857,X1858,X1859))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1857),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1856),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1855)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1855,X1857)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1855,X1856)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1856,esk9_5(X1855,X1856,X1857,X1858,X1859))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1857,esk9_5(X1855,X1856,X1857,X1858,X1859))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1857),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1856),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1855)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1855,X1856)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1855,X1857)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1856,esk9_5(X1855,X1856,X1857,X1858,X1859))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1857,esk9_5(X1855,X1856,X1857,X1858,X1859))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1857),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1856),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1855)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1855,X1857)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1855,X1856)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1856,esk9_5(X1855,X1856,X1857,X1858,X1859))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1858),X1859)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1857,esk9_5(X1855,X1856,X1857,X1858,X1859))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1857),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1856),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1855)) )
      & ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk10_1(X1861)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1861)) )
      & ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk11_1(X1861)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1861)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1861)),esk13_1(X1861))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X1861),X1866)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1861)),esk13_1(X1861))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X1861),X1866)))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1861)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1861)),esk13_1(X1861))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X1861),X1867)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1861)),esk13_1(X1861))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X1861),X1867)))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1861)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1861)),esk13_1(X1861))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1861,esk10_1(X1861))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1861)),esk13_1(X1861))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1861,esk11_1(X1861))))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1861)) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1861)),esk13_1(X1861))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1861,esk10_1(X1861))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1861)),esk13_1(X1861))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1861,esk11_1(X1861))))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1861)) ) ),
    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])])])])])]) ).

cnf(i_0_853,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]) ).

cnf(i_0_854,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]) ).

cnf(i_0_855,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2),X1))
    | ti(arrow_490897120le_alt,esk24_2(X1,X2)) != ti(arrow_490897120le_alt,esk25_2(X1,X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_628]) ).

fof(i_0_856,plain,
    ! [X2789,X2790,X2791] :
      ( ( hBOOL(hAPP(fun(X2789,bool),bool,finite_finite_1(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),collect(X2789),X2790)))
        | ~ hBOOL(hAPP(fun(X2789,bool),bool,finite_finite_1(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),collect(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),hAPP(fun(X2789,fun(bool,bool)),fun(fun(X2789,bool),fun(X2789,bool)),combs(X2789,bool,bool),hAPP(fun(X2789,bool),fun(X2789,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2789,bool),fun(X2789,fun(bool,bool))),combb(bool,fun(bool,bool),X2789),fdisj),X2790)),X2791)))) )
      & ( hBOOL(hAPP(fun(X2789,bool),bool,finite_finite_1(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),collect(X2789),X2791)))
        | ~ hBOOL(hAPP(fun(X2789,bool),bool,finite_finite_1(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),collect(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),hAPP(fun(X2789,fun(bool,bool)),fun(fun(X2789,bool),fun(X2789,bool)),combs(X2789,bool,bool),hAPP(fun(X2789,bool),fun(X2789,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2789,bool),fun(X2789,fun(bool,bool))),combb(bool,fun(bool,bool),X2789),fdisj),X2790)),X2791)))) )
      & ( ~ hBOOL(hAPP(fun(X2789,bool),bool,finite_finite_1(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),collect(X2789),X2790)))
        | ~ hBOOL(hAPP(fun(X2789,bool),bool,finite_finite_1(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),collect(X2789),X2791)))
        | hBOOL(hAPP(fun(X2789,bool),bool,finite_finite_1(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),collect(X2789),hAPP(fun(X2789,bool),fun(X2789,bool),hAPP(fun(X2789,fun(bool,bool)),fun(fun(X2789,bool),fun(X2789,bool)),combs(X2789,bool,bool),hAPP(fun(X2789,bool),fun(X2789,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2789,bool),fun(X2789,fun(bool,bool))),combb(bool,fun(bool,bool),X2789),fdisj),X2790)),X2791)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_289_finite__Collect__disjI])])]) ).

cnf(i_0_857,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]) ).

cnf(i_0_858,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk3_5(X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]) ).

cnf(i_0_859,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X3,X5,X2,X4,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk3_5(X3,X5,X2,X4,X1))))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_627]) ).

cnf(i_0_860,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_630]) ).

cnf(i_0_861,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_630]) ).

fof(i_0_862,plain,
    ! [X2862,X2863] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X2862)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2863))))),
    inference(variable_rename,[status(thm)],[fact_312_finite__M__bounded__by__nat]) ).

cnf(i_0_863,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X5),X4)))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_864,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_865,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X3,X4,X2,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X3,X4,X2,X1))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_630]) ).

cnf(i_0_866,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_630]) ).

fof(i_0_867,plain,
    ! [X2536,X2537,X2538,X2539,X2540] :
      ( ( hBOOL(hAPP(fun(X2537,bool),bool,hAPP(X2537,fun(fun(X2537,bool),bool),member(X2537),esk52_5(X2536,X2537,X2538,X2539,X2540)),X2540))
        | hBOOL(hAPP(fun(fun(X2537,X2536),bool),bool,hAPP(fun(fun(X2537,X2536),bool),fun(fun(fun(X2537,X2536),bool),bool),ord_less_eq(fun(fun(X2537,X2536),bool)),hAPP(fun(X2537,fun(X2536,bool)),fun(fun(X2537,X2536),bool),hAPP(fun(X2537,bool),fun(fun(X2537,fun(X2536,bool)),fun(fun(X2537,X2536),bool)),pi(X2537,X2536),X2540),X2538)),hAPP(fun(X2537,fun(X2536,bool)),fun(fun(X2537,X2536),bool),hAPP(fun(X2537,bool),fun(fun(X2537,fun(X2536,bool)),fun(fun(X2537,X2536),bool)),pi(X2537,X2536),X2540),X2539))) )
      & ( ~ hBOOL(hAPP(fun(X2536,bool),bool,hAPP(fun(X2536,bool),fun(fun(X2536,bool),bool),ord_less_eq(fun(X2536,bool)),hAPP(X2537,fun(X2536,bool),X2538,esk52_5(X2536,X2537,X2538,X2539,X2540))),hAPP(X2537,fun(X2536,bool),X2539,esk52_5(X2536,X2537,X2538,X2539,X2540))))
        | hBOOL(hAPP(fun(fun(X2537,X2536),bool),bool,hAPP(fun(fun(X2537,X2536),bool),fun(fun(fun(X2537,X2536),bool),bool),ord_less_eq(fun(fun(X2537,X2536),bool)),hAPP(fun(X2537,fun(X2536,bool)),fun(fun(X2537,X2536),bool),hAPP(fun(X2537,bool),fun(fun(X2537,fun(X2536,bool)),fun(fun(X2537,X2536),bool)),pi(X2537,X2536),X2540),X2538)),hAPP(fun(X2537,fun(X2536,bool)),fun(fun(X2537,X2536),bool),hAPP(fun(X2537,bool),fun(fun(X2537,fun(X2536,bool)),fun(fun(X2537,X2536),bool)),pi(X2537,X2536),X2540),X2539))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_210_Pi__mono])])])]) ).

fof(i_0_868,plain,
    ! [X2733,X2734,X2735,X2736,X2737,X2738] :
      ( ( ~ hBOOL(hAPP(fun(fun(X2734,X2733),bool),bool,hAPP(fun(X2734,X2733),fun(fun(fun(X2734,X2733),bool),bool),member(fun(X2734,X2733)),X2736),hAPP(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool),hAPP(fun(X2734,bool),fun(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool)),pi(X2734,X2733),X2738),X2735)))
        | hBOOL(hAPP(fun(fun(X2734,X2733),bool),bool,hAPP(fun(X2734,X2733),fun(fun(fun(X2734,X2733),bool),bool),member(fun(X2734,X2733)),X2737),hAPP(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool),hAPP(fun(X2734,bool),fun(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool)),pi(X2734,X2733),X2738),X2735)))
        | hBOOL(hAPP(fun(X2734,bool),bool,hAPP(X2734,fun(fun(X2734,bool),bool),member(X2734),esk67_6(X2733,X2734,X2735,X2736,X2737,X2738)),X2738)) )
      & ( ~ hBOOL(hAPP(fun(fun(X2734,X2733),bool),bool,hAPP(fun(X2734,X2733),fun(fun(fun(X2734,X2733),bool),bool),member(fun(X2734,X2733)),X2737),hAPP(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool),hAPP(fun(X2734,bool),fun(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool)),pi(X2734,X2733),X2738),X2735)))
        | hBOOL(hAPP(fun(fun(X2734,X2733),bool),bool,hAPP(fun(X2734,X2733),fun(fun(fun(X2734,X2733),bool),bool),member(fun(X2734,X2733)),X2736),hAPP(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool),hAPP(fun(X2734,bool),fun(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool)),pi(X2734,X2733),X2738),X2735)))
        | hBOOL(hAPP(fun(X2734,bool),bool,hAPP(X2734,fun(fun(X2734,bool),bool),member(X2734),esk67_6(X2733,X2734,X2735,X2736,X2737,X2738)),X2738)) )
      & ( ~ hBOOL(hAPP(fun(fun(X2734,X2733),bool),bool,hAPP(fun(X2734,X2733),fun(fun(fun(X2734,X2733),bool),bool),member(fun(X2734,X2733)),X2736),hAPP(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool),hAPP(fun(X2734,bool),fun(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool)),pi(X2734,X2733),X2738),X2735)))
        | hBOOL(hAPP(fun(fun(X2734,X2733),bool),bool,hAPP(fun(X2734,X2733),fun(fun(fun(X2734,X2733),bool),bool),member(fun(X2734,X2733)),X2737),hAPP(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool),hAPP(fun(X2734,bool),fun(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool)),pi(X2734,X2733),X2738),X2735)))
        | hAPP(X2734,X2733,X2736,esk67_6(X2733,X2734,X2735,X2736,X2737,X2738)) != hAPP(X2734,X2733,X2737,esk67_6(X2733,X2734,X2735,X2736,X2737,X2738)) )
      & ( ~ hBOOL(hAPP(fun(fun(X2734,X2733),bool),bool,hAPP(fun(X2734,X2733),fun(fun(fun(X2734,X2733),bool),bool),member(fun(X2734,X2733)),X2737),hAPP(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool),hAPP(fun(X2734,bool),fun(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool)),pi(X2734,X2733),X2738),X2735)))
        | hBOOL(hAPP(fun(fun(X2734,X2733),bool),bool,hAPP(fun(X2734,X2733),fun(fun(fun(X2734,X2733),bool),bool),member(fun(X2734,X2733)),X2736),hAPP(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool),hAPP(fun(X2734,bool),fun(fun(X2734,fun(X2733,bool)),fun(fun(X2734,X2733),bool)),pi(X2734,X2733),X2738),X2735)))
        | hAPP(X2734,X2733,X2736,esk67_6(X2733,X2734,X2735,X2736,X2737,X2738)) != hAPP(X2734,X2733,X2737,esk67_6(X2733,X2734,X2735,X2736,X2737,X2738)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_272_Pi__cong])])])]) ).

cnf(i_0_869,plain,
    ( ti(fun(product_prod(X1,X2),bool),X4) = ti(fun(product_prod(X1,X2),bool),X3)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))),X4))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_633]) ).

fof(i_0_870,plain,
    ! [X2780,X2781,X2782] :
      ( ( ~ hBOOL(hAPP(fun(X2780,bool),bool,finite_finite_1(X2780),hAPP(fun(X2780,bool),fun(X2780,bool),collect(X2780),X2782)))
        | hBOOL(hAPP(fun(X2780,bool),bool,finite_finite_1(X2780),hAPP(fun(X2780,bool),fun(X2780,bool),collect(X2780),hAPP(fun(X2780,bool),fun(X2780,bool),hAPP(fun(X2780,fun(bool,bool)),fun(fun(X2780,bool),fun(X2780,bool)),combs(X2780,bool,bool),hAPP(fun(X2780,bool),fun(X2780,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2780,bool),fun(X2780,fun(bool,bool))),combb(bool,fun(bool,bool),X2780),fconj),X2782)),X2781)))) )
      & ( ~ hBOOL(hAPP(fun(X2780,bool),bool,finite_finite_1(X2780),hAPP(fun(X2780,bool),fun(X2780,bool),collect(X2780),X2781)))
        | hBOOL(hAPP(fun(X2780,bool),bool,finite_finite_1(X2780),hAPP(fun(X2780,bool),fun(X2780,bool),collect(X2780),hAPP(fun(X2780,bool),fun(X2780,bool),hAPP(fun(X2780,fun(bool,bool)),fun(fun(X2780,bool),fun(X2780,bool)),combs(X2780,bool,bool),hAPP(fun(X2780,bool),fun(X2780,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2780,bool),fun(X2780,fun(bool,bool))),combb(bool,fun(bool,bool),X2780),fconj),X2782)),X2781)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_283_finite__Collect__conjI])])]) ).

fof(i_0_871,plain,
    ! [X2876,X2877] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk77_2(X2876,X2877)),hAPP(nat,nat,X2877,esk77_2(X2876,X2877))))
      | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X2877)),X2876)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_315_finite__less__ub])])]) ).

cnf(i_0_872,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]) ).

cnf(i_0_873,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X3)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_874,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_875,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X5),X4)))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_876,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_877,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X4),X5)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_878,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_879,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X5),X4)))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_880,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X5),X4)))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

fof(i_0_881,plain,
    ! [X2740,X2741,X2742,X2743,X2744] :
      ( ( hBOOL(hAPP(fun(X2741,bool),bool,hAPP(X2741,fun(fun(X2741,bool),bool),member(X2741),esk68_5(X2740,X2741,X2742,X2743,X2744)),X2744))
        | hBOOL(hAPP(fun(fun(X2741,X2740),bool),bool,hAPP(fun(X2741,X2740),fun(fun(fun(X2741,X2740),bool),bool),member(fun(X2741,X2740)),X2742),hAPP(fun(X2741,fun(X2740,bool)),fun(fun(X2741,X2740),bool),hAPP(fun(X2741,bool),fun(fun(X2741,fun(X2740,bool)),fun(fun(X2741,X2740),bool)),pi(X2741,X2740),X2744),X2743))) )
      & ( ~ hBOOL(hAPP(fun(X2740,bool),bool,hAPP(X2740,fun(fun(X2740,bool),bool),member(X2740),hAPP(X2741,X2740,X2742,esk68_5(X2740,X2741,X2742,X2743,X2744))),hAPP(X2741,fun(X2740,bool),X2743,esk68_5(X2740,X2741,X2742,X2743,X2744))))
        | hBOOL(hAPP(fun(fun(X2741,X2740),bool),bool,hAPP(fun(X2741,X2740),fun(fun(fun(X2741,X2740),bool),bool),member(fun(X2741,X2740)),X2742),hAPP(fun(X2741,fun(X2740,bool)),fun(fun(X2741,X2740),bool),hAPP(fun(X2741,bool),fun(fun(X2741,fun(X2740,bool)),fun(fun(X2741,X2740),bool)),pi(X2741,X2740),X2744),X2743))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_273_Pi__I_H])])])]) ).

fof(i_0_882,plain,
    ! [X2264,X2265,X2266,X2267,X2268] :
      ( ( hBOOL(hAPP(fun(X2265,bool),bool,hAPP(X2265,fun(fun(X2265,bool),bool),member(X2265),esk33_5(X2264,X2265,X2266,X2267,X2268)),X2268))
        | hBOOL(hAPP(fun(fun(X2265,X2264),bool),bool,hAPP(fun(X2265,X2264),fun(fun(fun(X2265,X2264),bool),bool),member(fun(X2265,X2264)),X2266),hAPP(fun(X2265,fun(X2264,bool)),fun(fun(X2265,X2264),bool),hAPP(fun(X2265,bool),fun(fun(X2265,fun(X2264,bool)),fun(fun(X2265,X2264),bool)),pi(X2265,X2264),X2268),X2267))) )
      & ( ~ hBOOL(hAPP(fun(X2264,bool),bool,hAPP(X2264,fun(fun(X2264,bool),bool),member(X2264),hAPP(X2265,X2264,X2266,esk33_5(X2264,X2265,X2266,X2267,X2268))),hAPP(X2265,fun(X2264,bool),X2267,esk33_5(X2264,X2265,X2266,X2267,X2268))))
        | hBOOL(hAPP(fun(fun(X2265,X2264),bool),bool,hAPP(fun(X2265,X2264),fun(fun(fun(X2265,X2264),bool),bool),member(fun(X2265,X2264)),X2266),hAPP(fun(X2265,fun(X2264,bool)),fun(fun(X2265,X2264),bool),hAPP(fun(X2265,bool),fun(fun(X2265,fun(X2264,bool)),fun(fun(X2265,X2264),bool)),pi(X2265,X2264),X2268),X2267))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_147_Pi__I])])])]) ).

fof(i_0_883,plain,
    ! [X3193,X3194] :
      ( ( ~ hBOOL(hAPP(X3193,bool,hAPP(X3193,fun(X3193,bool),ord_less(X3193),hAPP(X3193,X3193,hAPP(X3193,fun(X3193,X3193),plus_plus(X3193),hAPP(X3193,X3193,hAPP(X3193,fun(X3193,X3193),plus_plus(X3193),one_one(X3193)),X3194)),X3194)),zero_zero(X3193)))
        | hBOOL(hAPP(X3193,bool,hAPP(X3193,fun(X3193,bool),ord_less(X3193),X3194),zero_zero(X3193)))
        | ~ hBOOL(hAPP(fun(X3193,bool),bool,hAPP(X3193,fun(fun(X3193,bool),bool),member(X3193),X3194),ring_1_Ints(X3193)))
        | ~ linordered_idom(X3193) )
      & ( ~ hBOOL(hAPP(X3193,bool,hAPP(X3193,fun(X3193,bool),ord_less(X3193),X3194),zero_zero(X3193)))
        | hBOOL(hAPP(X3193,bool,hAPP(X3193,fun(X3193,bool),ord_less(X3193),hAPP(X3193,X3193,hAPP(X3193,fun(X3193,X3193),plus_plus(X3193),hAPP(X3193,X3193,hAPP(X3193,fun(X3193,X3193),plus_plus(X3193),one_one(X3193)),X3194)),X3194)),zero_zero(X3193)))
        | ~ hBOOL(hAPP(fun(X3193,bool),bool,hAPP(X3193,fun(fun(X3193,bool),bool),member(X3193),X3194),ring_1_Ints(X3193)))
        | ~ linordered_idom(X3193) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_457_Ints__odd__less__0])])])]) ).

cnf(i_0_884,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_885,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X3)),X5))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_886,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X4))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X2),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_887,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),X4))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X5),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_888,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X3),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_889,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_890,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_629]) ).

fof(i_0_891,plain,
    ! [X2821,X2822,X2823,X2824,X2825,X2826,X2827,X2828] :
      ( ~ hBOOL(hAPP(fun(fun(X2821,bool),X2822),bool,hAPP(fun(X2821,X2822),fun(fun(fun(X2821,bool),X2822),bool),hAPP(X2822,fun(fun(X2821,X2822),fun(fun(fun(X2821,bool),X2822),bool)),hAPP(fun(X2822,fun(X2822,X2822)),fun(X2822,fun(fun(X2821,X2822),fun(fun(fun(X2821,bool),X2822),bool))),finite908156982e_idem(X2822,X2821),X2825),X2826),X2827),X2828))
      | ~ hBOOL(hAPP(fun(X2821,bool),bool,finite_finite_1(X2821),X2824))
      | ~ hBOOL(hAPP(fun(X2821,bool),bool,hAPP(fun(X2821,bool),fun(fun(X2821,bool),bool),ord_less_eq(fun(X2821,bool)),X2823),X2824))
      | hAPP(X2822,X2822,hAPP(X2822,fun(X2822,X2822),X2825,hAPP(fun(X2821,bool),X2822,X2828,X2823)),hAPP(fun(X2821,bool),X2822,X2828,X2824)) = hAPP(fun(X2821,bool),X2822,X2828,X2824) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_303_folding__image__simple__idem_Osubset__idem])]) ).

fof(i_0_892,plain,
    ! [X2726,X2727,X2728,X2729,X2730] :
      ( ( hBOOL(hAPP(fun(X2727,bool),bool,hAPP(X2727,fun(fun(X2727,bool),bool),member(X2727),esk65_5(X2726,X2727,X2728,X2729,X2730)),X2730))
        | hBOOL(hAPP(fun(fun(X2727,X2726),bool),bool,hAPP(fun(X2727,X2726),fun(fun(fun(X2727,X2726),bool),bool),member(fun(X2727,X2726)),X2728),hAPP(fun(X2727,fun(X2726,bool)),fun(fun(X2727,X2726),bool),hAPP(fun(X2727,bool),fun(fun(X2727,fun(X2726,bool)),fun(fun(X2727,X2726),bool)),pi(X2727,X2726),X2730),hAPP(fun(X2726,bool),fun(X2727,fun(X2726,bool)),combk(fun(X2726,bool),X2727),X2729)))) )
      & ( ~ hBOOL(hAPP(fun(X2726,bool),bool,hAPP(X2726,fun(fun(X2726,bool),bool),member(X2726),hAPP(X2727,X2726,X2728,esk65_5(X2726,X2727,X2728,X2729,X2730))),X2729))
        | hBOOL(hAPP(fun(fun(X2727,X2726),bool),bool,hAPP(fun(X2727,X2726),fun(fun(fun(X2727,X2726),bool),bool),member(fun(X2727,X2726)),X2728),hAPP(fun(X2727,fun(X2726,bool)),fun(fun(X2727,X2726),bool),hAPP(fun(X2727,bool),fun(fun(X2727,fun(X2726,bool)),fun(fun(X2727,X2726),bool)),pi(X2727,X2726),X2730),hAPP(fun(X2726,bool),fun(X2727,fun(X2726,bool)),combk(fun(X2726,bool),X2727),X2729)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_270_funcsetI])])])]) ).

fof(i_0_893,plain,
    ! [X2852,X2853,X2854,X2855,X2856,X2857,X2858,X2859] :
      ( ~ hBOOL(hAPP(fun(fun(X2852,bool),X2853),bool,hAPP(fun(X2852,X2853),fun(fun(fun(X2852,bool),X2853),bool),hAPP(X2853,fun(fun(X2852,X2853),fun(fun(fun(X2852,bool),X2853),bool)),hAPP(fun(X2853,fun(X2853,X2853)),fun(X2853,fun(fun(X2852,X2853),fun(fun(fun(X2852,bool),X2853),bool))),finite908156982e_idem(X2853,X2852),X2856),X2857),X2858),X2859))
      | ~ hBOOL(hAPP(fun(X2852,bool),bool,finite_finite_1(X2852),X2855))
      | ~ hBOOL(hAPP(fun(X2852,bool),bool,hAPP(X2852,fun(fun(X2852,bool),bool),member(X2852),X2854),X2855))
      | hAPP(X2853,X2853,hAPP(X2853,fun(X2853,X2853),X2856,hAPP(X2852,X2853,X2858,X2854)),hAPP(fun(X2852,bool),X2853,X2859,X2855)) = hAPP(fun(X2852,bool),X2853,X2859,X2855) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_310_folding__image__simple__idem_Oin__idem])]) ).

cnf(i_0_894,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_895,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_896,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_897,plain,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X3)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_898,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_899,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X5),X4)))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

fof(i_0_900,plain,
    ! [X2763,X2764,X2765,X2766,X2767,X2768] :
      ( ~ hBOOL(hAPP(fun(fun(X2763,X2764),bool),bool,hAPP(fun(X2763,X2764),fun(fun(fun(X2763,X2764),bool),bool),member(fun(X2763,X2764)),X2766),hAPP(fun(X2763,fun(X2764,bool)),fun(fun(X2763,X2764),bool),hAPP(fun(X2763,bool),fun(fun(X2763,fun(X2764,bool)),fun(fun(X2763,X2764),bool)),pi(X2763,X2764),X2767),hAPP(fun(X2764,bool),fun(X2763,fun(X2764,bool)),combk(fun(X2764,bool),X2763),X2768))))
      | ~ hBOOL(hAPP(fun(X2763,bool),bool,hAPP(fun(X2763,X2764),fun(fun(X2763,bool),bool),inj_on(X2763,X2764),X2766),X2767))
      | ~ hBOOL(hAPP(fun(fun(X2764,X2763),bool),bool,hAPP(fun(X2764,X2763),fun(fun(fun(X2764,X2763),bool),bool),member(fun(X2764,X2763)),X2765),hAPP(fun(X2764,fun(X2763,bool)),fun(fun(X2764,X2763),bool),hAPP(fun(X2764,bool),fun(fun(X2764,fun(X2763,bool)),fun(fun(X2764,X2763),bool)),pi(X2764,X2763),X2768),hAPP(fun(X2763,bool),fun(X2764,fun(X2763,bool)),combk(fun(X2763,bool),X2764),X2767))))
      | ~ hBOOL(hAPP(fun(X2764,bool),bool,hAPP(fun(X2764,X2763),fun(fun(X2764,bool),bool),inj_on(X2764,X2763),X2765),X2768))
      | ~ hBOOL(hAPP(fun(X2763,bool),bool,finite_finite_1(X2763),X2767))
      | ~ hBOOL(hAPP(fun(X2764,bool),bool,finite_finite_1(X2764),X2768))
      | hAPP(fun(X2763,bool),nat,finite_card(X2763),X2767) = hAPP(fun(X2764,bool),nat,finite_card(X2764),X2768) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_278_card__bij])]) ).

cnf(i_0_901,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X4),X5)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_902,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X5),X4)))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_903,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X3),X2)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

cnf(i_0_904,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_905,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]) ).

cnf(i_0_906,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))),X4))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))),X3))
    | ti(fun(product_prod(X1,X2),bool),X4) = ti(fun(product_prod(X1,X2),bool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_633]) ).

cnf(i_0_907,plain,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_908,plain,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

fof(i_0_909,plain,
    ! [X1868,X1869,X1870,X1871,X1873,X1877] :
      ( ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1868))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1869),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1870),X1871)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1869,esk14_4(X1868,X1869,X1870,X1871))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1870),X1871)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1868,X1869))) )
      & ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk15_1(X1873)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1873)) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X1873)),esk17_1(X1873))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk15_1(X1873),X1877)))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1873)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X1873)),esk17_1(X1873))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1873,esk15_1(X1873))))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1873)) ) ),
    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])])])])])]) ).

cnf(i_0_910,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]) ).

cnf(i_0_911,plain,
    ( hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,X7),X7) = ti(X2,X7)
    | ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_634]) ).

cnf(i_0_912,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_629]) ).

cnf(i_0_913,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_635]) ).

cnf(i_0_914,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_636]) ).

fof(i_0_915,plain,
    ! [X3245,X3246,X3247,X3248] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3245,bool),nat,finite_card(X3245),hAPP(fun(X3246,bool),fun(X3245,bool),hAPP(fun(X3246,X3245),fun(fun(X3246,bool),fun(X3245,bool)),image(X3246,X3245),X3247),X3248))),hAPP(fun(X3246,bool),nat,finite_card(X3246),X3248)))
      | ~ hBOOL(hAPP(fun(X3246,bool),bool,hAPP(fun(X3246,X3245),fun(fun(X3246,bool),bool),inj_on(X3246,X3245),X3247),X3248)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_637])]) ).

cnf(i_0_916,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_629]) ).

cnf(i_0_917,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_638]) ).

fof(i_0_918,plain,
    ! [X1905,X1906,X1907] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1907),arrow_2064824852le_Lin))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1905),X1906)),X1907))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1906),X1905)),X1907)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_639])]) ).

fof(i_0_919,plain,
    ! [X2527,X2528,X2529] :
      ( ( ~ hBOOL(hAPP(fun(X2527,bool),bool,hAPP(fun(X2527,bool),fun(fun(X2527,bool),bool),ord_less_eq(fun(X2527,bool)),hAPP(fun(X2527,bool),fun(X2527,bool),hAPP(fun(X2527,fun(fun(X2527,bool),bool)),fun(fun(X2527,bool),fun(X2527,bool)),combc(X2527,fun(X2527,bool),bool),member(X2527)),X2528)),hAPP(fun(X2527,bool),fun(X2527,bool),hAPP(fun(X2527,fun(fun(X2527,bool),bool)),fun(fun(X2527,bool),fun(X2527,bool)),combc(X2527,fun(X2527,bool),bool),member(X2527)),X2529)))
        | hBOOL(hAPP(fun(X2527,bool),bool,hAPP(fun(X2527,bool),fun(fun(X2527,bool),bool),ord_less_eq(fun(X2527,bool)),X2528),X2529)) )
      & ( ~ hBOOL(hAPP(fun(X2527,bool),bool,hAPP(fun(X2527,bool),fun(fun(X2527,bool),bool),ord_less_eq(fun(X2527,bool)),X2528),X2529))
        | hBOOL(hAPP(fun(X2527,bool),bool,hAPP(fun(X2527,bool),fun(fun(X2527,bool),bool),ord_less_eq(fun(X2527,bool)),hAPP(fun(X2527,bool),fun(X2527,bool),hAPP(fun(X2527,fun(fun(X2527,bool),bool)),fun(fun(X2527,bool),fun(X2527,bool)),combc(X2527,fun(X2527,bool),bool),member(X2527)),X2528)),hAPP(fun(X2527,bool),fun(X2527,bool),hAPP(fun(X2527,fun(fun(X2527,bool),bool)),fun(fun(X2527,bool),fun(X2527,bool)),combc(X2527,fun(X2527,bool),bool),member(X2527)),X2529))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_208_pred__subset__eq])]) ).

fof(i_0_920,plain,
    ! [X3349,X3350,X3351,X3352,X3353] :
      ( ~ hBOOL(hAPP(fun(X3350,bool),bool,finite_finite_1(X3350),hAPP(fun(X3351,bool),fun(X3350,bool),hAPP(fun(X3351,X3350),fun(fun(X3351,bool),fun(X3350,bool)),image(X3351,X3350),X3353),top_top(fun(X3351,bool)))))
      | hBOOL(hAPP(fun(X3349,bool),bool,finite_finite_1(X3349),hAPP(fun(X3351,bool),fun(X3349,bool),hAPP(fun(X3351,X3349),fun(fun(X3351,bool),fun(X3349,bool)),image(X3351,X3349),hAPP(fun(X3351,X3350),fun(X3351,X3349),hAPP(fun(X3350,X3349),fun(fun(X3351,X3350),fun(X3351,X3349)),combb(X3350,X3349,X3351),X3352),X3353)),top_top(fun(X3351,bool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_493_finite__range__imageI])]) ).

cnf(i_0_921,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_640]) ).

cnf(i_0_922,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_641]) ).

cnf(i_0_923,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_631]) ).

cnf(i_0_924,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_632]) ).

fof(i_0_925,plain,
    ! [X3262,X3263,X3264,X3265,X3266] :
      ( ~ hBOOL(hAPP(fun(X3262,bool),bool,hAPP(X3262,fun(fun(X3262,bool),bool),member(X3262),X3264),hAPP(fun(X3263,bool),fun(X3262,bool),hAPP(fun(X3263,X3262),fun(fun(X3263,bool),fun(X3262,bool)),image(X3263,X3262),X3265),X3266)))
      | hBOOL(hAPP(fun(X3263,bool),bool,hAPP(X3263,fun(fun(X3263,bool),bool),member(X3263),hAPP(X3262,X3263,hAPP(fun(X3263,X3262),fun(X3262,X3263),hAPP(fun(X3263,bool),fun(fun(X3263,X3262),fun(X3262,X3263)),hilbert_inv_into(X3263,X3262),X3266),X3265),X3264)),X3266)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_478_inv__into__into])]) ).

fof(i_0_926,plain,
    ! [X2697,X2698,X2699] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk61_3(X2697,X2698,X2699)),esk62_3(X2697,X2698,X2699)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2699,X2697)),X2698)),hAPP(nat,nat,X2699,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2697),X2698)))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2699,esk61_3(X2697,X2698,X2699))),hAPP(nat,nat,X2699,esk62_3(X2697,X2698,X2699))))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2699,X2697)),X2698)),hAPP(nat,nat,X2699,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2697),X2698)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_262_mono__nat__linear__lb])])])]) ).

fof(i_0_927,plain,
    ! [X3159,X3160,X3161,X3162] :
      ( ( ~ hBOOL(hAPP(X3159,bool,hAPP(X3159,fun(X3159,bool),ord_less(X3159),hAPP(nat,X3159,X3162,X3160)),hAPP(nat,X3159,X3162,X3161)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3160),X3161))
        | ~ hBOOL(hAPP(X3159,bool,hAPP(X3159,fun(X3159,bool),ord_less(X3159),hAPP(nat,X3159,X3162,esk91_4(X3159,X3160,X3161,X3162))),hAPP(nat,X3159,X3162,hAPP(nat,nat,suc,esk91_4(X3159,X3160,X3161,X3162)))))
        | ~ order(X3159) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3160),X3161))
        | hBOOL(hAPP(X3159,bool,hAPP(X3159,fun(X3159,bool),ord_less(X3159),hAPP(nat,X3159,X3162,X3160)),hAPP(nat,X3159,X3162,X3161)))
        | ~ hBOOL(hAPP(X3159,bool,hAPP(X3159,fun(X3159,bool),ord_less(X3159),hAPP(nat,X3159,X3162,esk91_4(X3159,X3160,X3161,X3162))),hAPP(nat,X3159,X3162,hAPP(nat,nat,suc,esk91_4(X3159,X3160,X3161,X3162)))))
        | ~ order(X3159) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_443_lift__Suc__mono__less__iff])])])])]) ).

cnf(i_0_928,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_641]) ).

cnf(i_0_929,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_640]) ).

cnf(i_0_930,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_641]) ).

cnf(i_0_931,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_640]) ).

fof(i_0_932,plain,
    ! [X3213,X3214,X3215,X3216,X3217] :
      ( ~ hBOOL(hAPP(fun(fun(X3213,X3214),bool),bool,hAPP(fun(X3213,X3214),fun(fun(fun(X3213,X3214),bool),bool),member(fun(X3213,X3214)),X3215),hAPP(fun(X3213,fun(X3214,bool)),fun(fun(X3213,X3214),bool),hAPP(fun(X3213,bool),fun(fun(X3213,fun(X3214,bool)),fun(fun(X3213,X3214),bool)),pi(X3213,X3214),X3216),hAPP(fun(X3214,bool),fun(X3213,fun(X3214,bool)),combk(fun(X3214,bool),X3213),X3217))))
      | hBOOL(hAPP(fun(X3214,bool),bool,hAPP(fun(X3214,bool),fun(fun(X3214,bool),bool),ord_less_eq(fun(X3214,bool)),hAPP(fun(X3213,bool),fun(X3214,bool),hAPP(fun(X3213,X3214),fun(fun(X3213,bool),fun(X3214,bool)),image(X3213,X3214),X3215),X3216)),X3217)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_463_funcset__image])]) ).

fof(i_0_933,plain,
    ! [X3228,X3229,X3230,X3231,X3232] :
      ( ( ~ hBOOL(hAPP(fun(X3229,bool),bool,hAPP(fun(X3229,bool),fun(fun(X3229,bool),bool),ord_less_eq(fun(X3229,bool)),hAPP(fun(X3228,bool),fun(X3229,bool),hAPP(fun(X3228,X3229),fun(fun(X3228,bool),fun(X3229,bool)),image(X3228,X3229),X3232),X3230)),hAPP(fun(X3228,bool),fun(X3229,bool),hAPP(fun(X3228,X3229),fun(fun(X3228,bool),fun(X3229,bool)),image(X3228,X3229),X3232),X3231)))
        | hBOOL(hAPP(fun(X3228,bool),bool,hAPP(fun(X3228,bool),fun(fun(X3228,bool),bool),ord_less_eq(fun(X3228,bool)),X3230),X3231))
        | ~ hBOOL(hAPP(fun(X3228,bool),bool,hAPP(fun(X3228,X3229),fun(fun(X3228,bool),bool),inj_on(X3228,X3229),X3232),top_top(fun(X3228,bool)))) )
      & ( ~ hBOOL(hAPP(fun(X3228,bool),bool,hAPP(fun(X3228,bool),fun(fun(X3228,bool),bool),ord_less_eq(fun(X3228,bool)),X3230),X3231))
        | hBOOL(hAPP(fun(X3229,bool),bool,hAPP(fun(X3229,bool),fun(fun(X3229,bool),bool),ord_less_eq(fun(X3229,bool)),hAPP(fun(X3228,bool),fun(X3229,bool),hAPP(fun(X3228,X3229),fun(fun(X3228,bool),fun(X3229,bool)),image(X3228,X3229),X3232),X3230)),hAPP(fun(X3228,bool),fun(X3229,bool),hAPP(fun(X3228,X3229),fun(fun(X3228,bool),fun(X3229,bool)),image(X3228,X3229),X3232),X3231)))
        | ~ hBOOL(hAPP(fun(X3228,bool),bool,hAPP(fun(X3228,X3229),fun(fun(X3228,bool),bool),inj_on(X3228,X3229),X3232),top_top(fun(X3228,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_468_inj__image__subset__iff])])]) ).

fof(i_0_934,plain,
    ! [X3149,X3150,X3151,X3152] :
      ( ~ order(X3149)
      | ~ hBOOL(hAPP(X3149,bool,hAPP(X3149,fun(X3149,bool),ord_less_eq(X3149),hAPP(nat,X3149,X3152,esk89_4(X3149,X3150,X3151,X3152))),hAPP(nat,X3149,X3152,hAPP(nat,nat,suc,esk89_4(X3149,X3150,X3151,X3152)))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3150),X3151))
      | hBOOL(hAPP(X3149,bool,hAPP(X3149,fun(X3149,bool),ord_less_eq(X3149),hAPP(nat,X3149,X3152,X3150)),hAPP(nat,X3149,X3152,X3151))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_441_lift__Suc__mono__le])])])]) ).

fof(i_0_935,plain,
    ! [X3154,X3155,X3156,X3157] :
      ( ~ order(X3154)
      | ~ hBOOL(hAPP(X3154,bool,hAPP(X3154,fun(X3154,bool),ord_less(X3154),hAPP(nat,X3154,X3157,esk90_4(X3154,X3155,X3156,X3157))),hAPP(nat,X3154,X3157,hAPP(nat,nat,suc,esk90_4(X3154,X3155,X3156,X3157)))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3155),X3156))
      | hBOOL(hAPP(X3154,bool,hAPP(X3154,fun(X3154,bool),ord_less(X3154),hAPP(nat,X3154,X3157,X3155)),hAPP(nat,X3154,X3157,X3156))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_442_lift__Suc__mono__less])])])]) ).

fof(i_0_936,plain,
    ! [X3354,X3355] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X3354),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3355),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3355),hAPP(fun(nat,bool),nat,finite_card(nat),X3354)))))
      | X3354 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3355),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3355),hAPP(fun(nat,bool),nat,finite_card(nat),X3354))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_494_subset__card__intvl__is__intvl])]) ).

cnf(i_0_937,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X6))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5))
    | ti(fun(product_prod(X1,X2),bool),X5) != ti(fun(product_prod(X1,X2),bool),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_633]) ).

cnf(i_0_938,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X6))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5))
    | ti(fun(product_prod(X1,X2),bool),X6) != ti(fun(product_prod(X1,X2),bool),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_633]) ).

fof(i_0_939,plain,
    ! [X2746,X2747,X2748,X2749,X2750] :
      ( ~ hBOOL(hAPP(fun(fun(X2746,X2747),bool),bool,hAPP(fun(X2746,X2747),fun(fun(fun(X2746,X2747),bool),bool),member(fun(X2746,X2747)),X2748),hAPP(fun(X2746,fun(X2747,bool)),fun(fun(X2746,X2747),bool),hAPP(fun(X2746,bool),fun(fun(X2746,fun(X2747,bool)),fun(fun(X2746,X2747),bool)),pi(X2746,X2747),X2749),hAPP(fun(X2747,bool),fun(X2746,fun(X2747,bool)),combk(fun(X2747,bool),X2746),X2750))))
      | ~ hBOOL(hAPP(fun(X2746,bool),bool,hAPP(fun(X2746,X2747),fun(fun(X2746,bool),bool),inj_on(X2746,X2747),X2748),X2749))
      | ~ hBOOL(hAPP(fun(X2747,bool),bool,finite_finite_1(X2747),X2750))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X2746,bool),nat,finite_card(X2746),X2749)),hAPP(fun(X2747,bool),nat,finite_card(X2747),X2750))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_274_card__inj])]) ).

cnf(i_0_940,plain,
    ( ti(X1,X5) = ti(X1,X6)
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X5) != hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_642]) ).

fof(i_0_941,plain,
    ! [X2229,X2230,X2231,X2232,X2233,X2234] :
      ( ~ hBOOL(hAPP(fun(fun(X2229,X2230),bool),bool,hAPP(fun(X2229,X2230),fun(fun(fun(X2229,X2230),bool),bool),member(fun(X2229,X2230)),X2232),hAPP(fun(X2229,fun(X2230,bool)),fun(fun(X2229,X2230),bool),hAPP(fun(X2229,bool),fun(fun(X2229,fun(X2230,bool)),fun(fun(X2229,X2230),bool)),pi(X2229,X2230),X2233),hAPP(fun(X2230,bool),fun(X2229,fun(X2230,bool)),combk(fun(X2230,bool),X2229),X2234))))
      | ~ hBOOL(hAPP(fun(X2229,bool),bool,hAPP(X2229,fun(fun(X2229,bool),bool),member(X2229),X2231),X2233))
      | hBOOL(hAPP(fun(X2230,bool),bool,hAPP(X2230,fun(fun(X2230,bool),bool),member(X2230),hAPP(X2229,X2230,X2232,X2231)),X2234)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_140_funcset__mem])]) ).

cnf(i_0_942,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_638]) ).

fof(i_0_943,plain,
    ! [X2305,X2306,X2307,X2308,X2309] :
      ( ~ hBOOL(hAPP(fun(X2306,bool),bool,hAPP(fun(X2306,bool),fun(fun(X2306,bool),bool),ord_less_eq(fun(X2306,bool)),X2308),X2309))
      | hBOOL(hAPP(fun(fun(X2306,X2305),bool),bool,hAPP(fun(fun(X2306,X2305),bool),fun(fun(fun(X2306,X2305),bool),bool),ord_less_eq(fun(fun(X2306,X2305),bool)),hAPP(fun(X2306,fun(X2305,bool)),fun(fun(X2306,X2305),bool),hAPP(fun(X2306,bool),fun(fun(X2306,fun(X2305,bool)),fun(fun(X2306,X2305),bool)),pi(X2306,X2305),X2309),X2307)),hAPP(fun(X2306,fun(X2305,bool)),fun(fun(X2306,X2305),bool),hAPP(fun(X2306,bool),fun(fun(X2306,fun(X2305,bool)),fun(fun(X2306,X2305),bool)),pi(X2306,X2305),X2308),X2307))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_156_Pi__anti__mono])]) ).

cnf(i_0_944,plain,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_640]) ).

cnf(i_0_945,plain,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_641]) ).

cnf(i_0_946,plain,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_641]) ).

cnf(i_0_947,plain,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_640]) ).

fof(i_0_948,plain,
    ! [X3208,X3209,X3210,X3211,X3212] :
      ( ( hBOOL(hAPP(X3208,bool,hAPP(X3208,fun(X3208,bool),ord_less_eq(X3208),X3211),X3209))
        | hBOOL(hAPP(X3208,bool,hAPP(X3208,fun(X3208,bool),ord_less_eq(X3208),X3210),X3209))
        | ~ hBOOL(hAPP(fun(X3208,bool),bool,hAPP(fun(X3208,bool),fun(fun(X3208,bool),bool),ord_less_eq(fun(X3208,bool)),hAPP(X3208,fun(X3208,bool),hAPP(X3208,fun(X3208,fun(X3208,bool)),ord_atLeastLessThan(X3208),X3209),X3210)),hAPP(X3208,fun(X3208,bool),hAPP(X3208,fun(X3208,fun(X3208,bool)),ord_atLeastLessThan(X3208),X3211),X3212)))
        | ~ linorder(X3208) )
      & ( hBOOL(hAPP(X3208,bool,hAPP(X3208,fun(X3208,bool),ord_less_eq(X3208),X3210),X3212))
        | hBOOL(hAPP(X3208,bool,hAPP(X3208,fun(X3208,bool),ord_less_eq(X3208),X3210),X3209))
        | ~ hBOOL(hAPP(fun(X3208,bool),bool,hAPP(fun(X3208,bool),fun(fun(X3208,bool),bool),ord_less_eq(fun(X3208,bool)),hAPP(X3208,fun(X3208,bool),hAPP(X3208,fun(X3208,fun(X3208,bool)),ord_atLeastLessThan(X3208),X3209),X3210)),hAPP(X3208,fun(X3208,bool),hAPP(X3208,fun(X3208,fun(X3208,bool)),ord_atLeastLessThan(X3208),X3211),X3212)))
        | ~ linorder(X3208) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_462_atLeastLessThan__subset__iff])])])]) ).

fof(i_0_949,plain,
    ! [X3233,X3234,X3235,X3236] :
      ( ~ hBOOL(hAPP(fun(X3234,bool),bool,finite_finite_1(X3234),X3236))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3233,bool),nat,finite_card(X3233),hAPP(fun(X3234,bool),fun(X3233,bool),hAPP(fun(X3234,X3233),fun(fun(X3234,bool),fun(X3233,bool)),image(X3234,X3233),X3235),X3236))),hAPP(fun(X3234,bool),nat,finite_card(X3234),X3236))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_469_card__image__le])]) ).

cnf(i_0_950,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X3),X2) = ti(fun(X1,bool),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X3),X2)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_643]) ).

fof(i_0_951,plain,
    ! [X2221,X2222,X2223,X2224,X2225,X2226] :
      ( ~ hBOOL(hAPP(fun(fun(X2221,X2222),bool),bool,hAPP(fun(X2221,X2222),fun(fun(fun(X2221,X2222),bool),bool),member(fun(X2221,X2222)),X2224),hAPP(fun(X2221,fun(X2222,bool)),fun(fun(X2221,X2222),bool),hAPP(fun(X2221,bool),fun(fun(X2221,fun(X2222,bool)),fun(fun(X2221,X2222),bool)),pi(X2221,X2222),X2225),X2226)))
      | ~ hBOOL(hAPP(fun(X2221,bool),bool,hAPP(X2221,fun(fun(X2221,bool),bool),member(X2221),X2223),X2225))
      | hBOOL(hAPP(fun(X2222,bool),bool,hAPP(X2222,fun(fun(X2222,bool),bool),member(X2222),hAPP(X2221,X2222,X2224,X2223)),hAPP(X2221,fun(X2222,bool),X2226,X2223))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_Pi__mem])]) ).

fof(i_0_952,plain,
    ! [X2033,X2034,X2035,X2036,X2037,X2038] :
      ( ~ hBOOL(hAPP(fun(fun(X2033,X2034),bool),bool,hAPP(fun(X2033,X2034),fun(fun(fun(X2033,X2034),bool),bool),member(fun(X2033,X2034)),X2036),hAPP(fun(X2033,fun(X2034,bool)),fun(fun(X2033,X2034),bool),hAPP(fun(X2033,bool),fun(fun(X2033,fun(X2034,bool)),fun(fun(X2033,X2034),bool)),pi(X2033,X2034),X2037),X2038)))
      | hBOOL(hAPP(fun(X2034,bool),bool,hAPP(X2034,fun(fun(X2034,bool),bool),member(X2034),hAPP(X2033,X2034,X2036,X2035)),hAPP(X2033,fun(X2034,bool),X2038,X2035)))
      | ~ hBOOL(hAPP(fun(X2033,bool),bool,hAPP(X2033,fun(fun(X2033,bool),bool),member(X2033),X2035),X2037)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_644])]) ).

fof(i_0_953,plain,
    ! [X3356,X3357,X3358,X3359,X3360] :
      ( ~ hBOOL(hAPP(fun(X3356,bool),bool,hAPP(fun(X3356,X3357),fun(fun(X3356,bool),bool),inj_on(X3356,X3357),X3359),X3360))
      | ~ hBOOL(hAPP(fun(X3356,bool),bool,hAPP(fun(X3356,bool),fun(fun(X3356,bool),bool),ord_less(fun(X3356,bool)),X3358),X3360))
      | hBOOL(hAPP(fun(X3357,bool),bool,hAPP(fun(X3357,bool),fun(fun(X3357,bool),bool),ord_less(fun(X3357,bool)),hAPP(fun(X3356,bool),fun(X3357,bool),hAPP(fun(X3356,X3357),fun(fun(X3356,bool),fun(X3357,bool)),image(X3356,X3357),X3359),X3358)),hAPP(fun(X3356,bool),fun(X3357,bool),hAPP(fun(X3356,X3357),fun(fun(X3356,bool),fun(X3357,bool)),image(X3356,X3357),X3359),X3360))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_495_inj__on__strict__subset])]) ).

fof(i_0_954,plain,
    ! [X2805,X2806] :
      ( ( ~ hBOOL(hAPP(fun(X2805,bool),bool,finite_finite_1(X2805),hAPP(fun(X2805,bool),fun(X2805,bool),collect(X2805),hAPP(fun(X2805,bool),fun(X2805,bool),hAPP(fun(bool,bool),fun(fun(X2805,bool),fun(X2805,bool)),combb(bool,bool,X2805),fNot),X2806))))
        | hBOOL(hAPP(fun(X2805,bool),bool,finite_finite_1(X2805),top_top(fun(X2805,bool))))
        | ~ hBOOL(hAPP(fun(X2805,bool),bool,finite_finite_1(X2805),hAPP(fun(X2805,bool),fun(X2805,bool),collect(X2805),X2806))) )
      & ( ~ hBOOL(hAPP(fun(X2805,bool),bool,finite_finite_1(X2805),top_top(fun(X2805,bool))))
        | hBOOL(hAPP(fun(X2805,bool),bool,finite_finite_1(X2805),hAPP(fun(X2805,bool),fun(X2805,bool),collect(X2805),hAPP(fun(X2805,bool),fun(X2805,bool),hAPP(fun(bool,bool),fun(fun(X2805,bool),fun(X2805,bool)),combb(bool,bool,X2805),fNot),X2806))))
        | ~ hBOOL(hAPP(fun(X2805,bool),bool,finite_finite_1(X2805),hAPP(fun(X2805,bool),fun(X2805,bool),collect(X2805),X2806))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_297_finite__Collect__not])])]) ).

fof(i_0_955,plain,
    ! [X2721,X2722,X2723,X2724,X2725] :
      ( ( ~ hBOOL(hAPP(X2721,bool,hAPP(X2722,fun(X2721,bool),hAPP(fun(product_prod(X2722,X2721),bool),fun(X2722,fun(X2721,bool)),in_rel(X2722,X2721),X2723),X2724),X2725))
        | hBOOL(hAPP(fun(product_prod(X2722,X2721),bool),bool,hAPP(product_prod(X2722,X2721),fun(fun(product_prod(X2722,X2721),bool),bool),member(product_prod(X2722,X2721)),hAPP(X2721,product_prod(X2722,X2721),hAPP(X2722,fun(X2721,product_prod(X2722,X2721)),product_Pair(X2722,X2721),X2724),X2725)),X2723)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X2722,X2721),bool),bool,hAPP(product_prod(X2722,X2721),fun(fun(product_prod(X2722,X2721),bool),bool),member(product_prod(X2722,X2721)),hAPP(X2721,product_prod(X2722,X2721),hAPP(X2722,fun(X2721,product_prod(X2722,X2721)),product_Pair(X2722,X2721),X2724),X2725)),X2723))
        | hBOOL(hAPP(X2721,bool,hAPP(X2722,fun(X2721,bool),hAPP(fun(product_prod(X2722,X2721),bool),fun(X2722,fun(X2721,bool)),in_rel(X2722,X2721),X2723),X2724),X2725)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_269_in__rel__def])]) ).

fof(i_0_956,plain,
    ! [X2769,X2770] :
      ( ~ hBOOL(hAPP(fun(X2769,bool),bool,finite_finite_1(X2769),X2770))
      | hBOOL(hAPP(fun(fun(X2769,bool),bool),bool,finite_finite_1(fun(X2769,bool)),hAPP(fun(fun(X2769,bool),bool),fun(fun(X2769,bool),bool),collect(fun(X2769,bool)),hAPP(fun(X2769,bool),fun(fun(X2769,bool),bool),hAPP(fun(fun(X2769,bool),fun(fun(X2769,bool),bool)),fun(fun(X2769,bool),fun(fun(X2769,bool),bool)),combc(fun(X2769,bool),fun(X2769,bool),bool),ord_less_eq(fun(X2769,bool))),X2770)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_279_finite__Collect__subsets])]) ).

fof(i_0_957,plain,
    ! [X2045,X2046,X2047,X2048] :
      ( ~ hBOOL(hAPP(fun(X2046,bool),bool,hAPP(fun(X2046,X2047),fun(fun(X2046,bool),bool),inj_on(X2046,X2047),X2048),top_top(fun(X2046,bool))))
      | hBOOL(hAPP(fun(X2046,bool),bool,hAPP(fun(X2046,fun(X2045,X2047)),fun(fun(X2046,bool),bool),inj_on(X2046,fun(X2045,X2047)),hAPP(fun(X2046,X2047),fun(X2046,fun(X2045,X2047)),hAPP(fun(X2047,fun(X2045,X2047)),fun(fun(X2046,X2047),fun(X2046,fun(X2045,X2047))),combb(X2047,fun(X2045,X2047),X2046),combk(X2047,X2045)),X2048)),top_top(fun(X2046,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_89_inj__fun])]) ).

fof(i_0_958,plain,
    ! [X1908,X1909] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1909),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1909),X1908)),arrow_2064824852le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_mktop__Lin])]) ).

fof(i_0_959,plain,
    ! [X1910,X1911] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1911),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1911),X1910)),arrow_2064824852le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_49_mkbot__Lin])]) ).

fof(i_0_960,plain,
    ! [X2375,X2376,X2377,X2378] :
      ( ( ~ hBOOL(hAPP(X2375,bool,hAPP(X2375,fun(X2375,bool),ord_less_eq(X2375),hAPP(X2375,X2375,hAPP(X2375,fun(X2375,X2375),plus_plus(X2375),X2376),X2377)),hAPP(X2375,X2375,hAPP(X2375,fun(X2375,X2375),plus_plus(X2375),X2378),X2377)))
        | hBOOL(hAPP(X2375,bool,hAPP(X2375,fun(X2375,bool),ord_less_eq(X2375),X2376),X2378))
        | ~ ordere236663937imp_le(X2375) )
      & ( ~ hBOOL(hAPP(X2375,bool,hAPP(X2375,fun(X2375,bool),ord_less_eq(X2375),X2376),X2378))
        | hBOOL(hAPP(X2375,bool,hAPP(X2375,fun(X2375,bool),ord_less_eq(X2375),hAPP(X2375,X2375,hAPP(X2375,fun(X2375,X2375),plus_plus(X2375),X2376),X2377)),hAPP(X2375,X2375,hAPP(X2375,fun(X2375,X2375),plus_plus(X2375),X2378),X2377)))
        | ~ ordere236663937imp_le(X2375) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_174_add__le__cancel__right])])])]) ).

fof(i_0_961,plain,
    ! [X2354,X2355,X2356,X2357] :
      ( ~ ordere236663937imp_le(X2354)
      | ~ hBOOL(hAPP(X2354,bool,hAPP(X2354,fun(X2354,bool),ord_less_eq(X2354),hAPP(X2354,X2354,hAPP(X2354,fun(X2354,X2354),plus_plus(X2354),X2355),X2356)),hAPP(X2354,X2354,hAPP(X2354,fun(X2354,X2354),plus_plus(X2354),X2357),X2356)))
      | hBOOL(hAPP(X2354,bool,hAPP(X2354,fun(X2354,bool),ord_less_eq(X2354),X2355),X2357)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_169_add__le__imp__le__right])])]) ).

fof(i_0_962,plain,
    ! [X2371,X2372,X2373,X2374] :
      ( ( ~ hBOOL(hAPP(X2371,bool,hAPP(X2371,fun(X2371,bool),ord_less_eq(X2371),hAPP(X2371,X2371,hAPP(X2371,fun(X2371,X2371),plus_plus(X2371),X2372),X2373)),hAPP(X2371,X2371,hAPP(X2371,fun(X2371,X2371),plus_plus(X2371),X2372),X2374)))
        | hBOOL(hAPP(X2371,bool,hAPP(X2371,fun(X2371,bool),ord_less_eq(X2371),X2373),X2374))
        | ~ ordere236663937imp_le(X2371) )
      & ( ~ hBOOL(hAPP(X2371,bool,hAPP(X2371,fun(X2371,bool),ord_less_eq(X2371),X2373),X2374))
        | hBOOL(hAPP(X2371,bool,hAPP(X2371,fun(X2371,bool),ord_less_eq(X2371),hAPP(X2371,X2371,hAPP(X2371,fun(X2371,X2371),plus_plus(X2371),X2372),X2373)),hAPP(X2371,X2371,hAPP(X2371,fun(X2371,X2371),plus_plus(X2371),X2372),X2374)))
        | ~ ordere236663937imp_le(X2371) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_173_add__le__cancel__left])])])]) ).

fof(i_0_963,plain,
    ! [X2350,X2351,X2352,X2353] :
      ( ~ ordere236663937imp_le(X2350)
      | ~ hBOOL(hAPP(X2350,bool,hAPP(X2350,fun(X2350,bool),ord_less_eq(X2350),hAPP(X2350,X2350,hAPP(X2350,fun(X2350,X2350),plus_plus(X2350),X2351),X2352)),hAPP(X2350,X2350,hAPP(X2350,fun(X2350,X2350),plus_plus(X2350),X2351),X2353)))
      | hBOOL(hAPP(X2350,bool,hAPP(X2350,fun(X2350,bool),ord_less_eq(X2350),X2352),X2353)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_168_add__le__imp__le__left])])]) ).

fof(i_0_964,plain,
    ! [X2404,X2405,X2406,X2407] :
      ( ( ~ hBOOL(hAPP(X2404,bool,hAPP(X2404,fun(X2404,bool),ord_less(X2404),hAPP(X2404,X2404,hAPP(X2404,fun(X2404,X2404),plus_plus(X2404),X2405),X2406)),hAPP(X2404,X2404,hAPP(X2404,fun(X2404,X2404),plus_plus(X2404),X2407),X2406)))
        | hBOOL(hAPP(X2404,bool,hAPP(X2404,fun(X2404,bool),ord_less(X2404),X2405),X2407))
        | ~ ordere236663937imp_le(X2404) )
      & ( ~ hBOOL(hAPP(X2404,bool,hAPP(X2404,fun(X2404,bool),ord_less(X2404),X2405),X2407))
        | hBOOL(hAPP(X2404,bool,hAPP(X2404,fun(X2404,bool),ord_less(X2404),hAPP(X2404,X2404,hAPP(X2404,fun(X2404,X2404),plus_plus(X2404),X2405),X2406)),hAPP(X2404,X2404,hAPP(X2404,fun(X2404,X2404),plus_plus(X2404),X2407),X2406)))
        | ~ ordere236663937imp_le(X2404) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_181_add__less__cancel__right])])])]) ).

fof(i_0_965,plain,
    ! [X2383,X2384,X2385,X2386] :
      ( ~ ordere236663937imp_le(X2383)
      | ~ hBOOL(hAPP(X2383,bool,hAPP(X2383,fun(X2383,bool),ord_less(X2383),hAPP(X2383,X2383,hAPP(X2383,fun(X2383,X2383),plus_plus(X2383),X2384),X2385)),hAPP(X2383,X2383,hAPP(X2383,fun(X2383,X2383),plus_plus(X2383),X2386),X2385)))
      | hBOOL(hAPP(X2383,bool,hAPP(X2383,fun(X2383,bool),ord_less(X2383),X2384),X2386)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_176_add__less__imp__less__right])])]) ).

fof(i_0_966,plain,
    ! [X2400,X2401,X2402,X2403] :
      ( ( ~ hBOOL(hAPP(X2400,bool,hAPP(X2400,fun(X2400,bool),ord_less(X2400),hAPP(X2400,X2400,hAPP(X2400,fun(X2400,X2400),plus_plus(X2400),X2401),X2402)),hAPP(X2400,X2400,hAPP(X2400,fun(X2400,X2400),plus_plus(X2400),X2401),X2403)))
        | hBOOL(hAPP(X2400,bool,hAPP(X2400,fun(X2400,bool),ord_less(X2400),X2402),X2403))
        | ~ ordere236663937imp_le(X2400) )
      & ( ~ hBOOL(hAPP(X2400,bool,hAPP(X2400,fun(X2400,bool),ord_less(X2400),X2402),X2403))
        | hBOOL(hAPP(X2400,bool,hAPP(X2400,fun(X2400,bool),ord_less(X2400),hAPP(X2400,X2400,hAPP(X2400,fun(X2400,X2400),plus_plus(X2400),X2401),X2402)),hAPP(X2400,X2400,hAPP(X2400,fun(X2400,X2400),plus_plus(X2400),X2401),X2403)))
        | ~ ordere236663937imp_le(X2400) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_180_add__less__cancel__left])])])]) ).

fof(i_0_967,plain,
    ! [X2379,X2380,X2381,X2382] :
      ( ~ ordere236663937imp_le(X2379)
      | ~ hBOOL(hAPP(X2379,bool,hAPP(X2379,fun(X2379,bool),ord_less(X2379),hAPP(X2379,X2379,hAPP(X2379,fun(X2379,X2379),plus_plus(X2379),X2380),X2381)),hAPP(X2379,X2379,hAPP(X2379,fun(X2379,X2379),plus_plus(X2379),X2380),X2382)))
      | hBOOL(hAPP(X2379,bool,hAPP(X2379,fun(X2379,bool),ord_less(X2379),X2381),X2382)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_175_add__less__imp__less__left])])]) ).

fof(i_0_968,plain,
    ! [X3315,X3316,X3317,X3318,X3319] :
      ( ~ hBOOL(hAPP(fun(X3316,bool),bool,hAPP(fun(X3316,bool),fun(fun(X3316,bool),bool),ord_less_eq(fun(X3316,bool)),X3318),X3319))
      | hBOOL(hAPP(fun(X3315,bool),bool,hAPP(fun(X3315,bool),fun(fun(X3315,bool),bool),ord_less_eq(fun(X3315,bool)),hAPP(fun(X3316,bool),fun(X3315,bool),hAPP(fun(X3316,X3315),fun(fun(X3316,bool),fun(X3315,bool)),image(X3316,X3315),X3317),X3318)),hAPP(fun(X3316,bool),fun(X3315,bool),hAPP(fun(X3316,X3315),fun(fun(X3316,bool),fun(X3315,bool)),image(X3316,X3315),X3317),X3319))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_486_image__mono])]) ).

fof(i_0_969,plain,
    ! [X2681,X2682,X2683] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2681),X2682)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2681),X2683)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2682),X2683)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2682),X2683))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2681),X2682)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2681),X2683))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_257_nat__add__left__cancel__le])]) ).

fof(i_0_970,plain,
    ! [X2638,X2639,X2640] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2638),X2639)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2638),X2640)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2639),X2640)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2639),X2640))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2638),X2639)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2638),X2640))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_242_nat__add__left__cancel__less])]) ).

fof(i_0_971,plain,
    ! [X2408,X2409,X2410,X2411] :
      ( ~ ord(X2409)
      | ~ hBOOL(hAPP(X2409,bool,hAPP(X2409,fun(X2409,bool),ord_less_eq(X2409),hAPP(X2408,X2409,X2410,esk39_4(X2408,X2409,X2410,X2411))),hAPP(X2408,X2409,X2411,esk39_4(X2408,X2409,X2410,X2411))))
      | hBOOL(hAPP(fun(X2408,X2409),bool,hAPP(fun(X2408,X2409),fun(fun(X2408,X2409),bool),ord_less_eq(fun(X2408,X2409)),X2410),X2411)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_182_le__funI])])])]) ).

fof(i_0_972,plain,
    ! [X2110,X2111,X2112,X2113,X2114,X2115,X2116] :
      ( ( ~ hBOOL(hAPP(fun(X2110,X2111),bool,hAPP(fun(X2110,X2111),fun(fun(X2110,X2111),bool),ord_less_eq(fun(X2110,X2111)),X2112),X2113))
        | hBOOL(hAPP(X2111,bool,hAPP(X2111,fun(X2111,bool),ord_less_eq(X2111),hAPP(X2110,X2111,X2112,X2114)),hAPP(X2110,X2111,X2113,X2114)))
        | ~ ord(X2111) )
      & ( ~ hBOOL(hAPP(X2111,bool,hAPP(X2111,fun(X2111,bool),ord_less_eq(X2111),hAPP(X2110,X2111,X2115,esk29_4(X2110,X2111,X2115,X2116))),hAPP(X2110,X2111,X2116,esk29_4(X2110,X2111,X2115,X2116))))
        | hBOOL(hAPP(fun(X2110,X2111),bool,hAPP(fun(X2110,X2111),fun(fun(X2110,X2111),bool),ord_less_eq(fun(X2110,X2111)),X2115),X2116))
        | ~ ord(X2111) ) ),
    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_108_le__fun__def])])])])])]) ).

fof(i_0_973,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(i_0_974,plain,
    ! [X1915] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1915),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X1915)),arrow_1111136790e_Prof)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_const__Lin__Prof])]) ).

fof(i_0_975,plain,
    ! [X2757,X2758,X2759,X2760,X2761] :
      ( ( ~ hBOOL(hAPP(fun(X2758,bool),bool,hAPP(fun(X2758,X2757),fun(fun(X2758,bool),bool),inj_on(X2758,X2757),X2759),X2761))
        | hBOOL(hAPP(fun(X2758,bool),bool,hAPP(fun(X2758,X2757),fun(fun(X2758,bool),bool),inj_on(X2758,X2757),X2760),X2761))
        | hBOOL(hAPP(fun(X2758,bool),bool,hAPP(X2758,fun(fun(X2758,bool),bool),member(X2758),esk71_5(X2757,X2758,X2759,X2760,X2761)),X2761)) )
      & ( ~ hBOOL(hAPP(fun(X2758,bool),bool,hAPP(fun(X2758,X2757),fun(fun(X2758,bool),bool),inj_on(X2758,X2757),X2760),X2761))
        | hBOOL(hAPP(fun(X2758,bool),bool,hAPP(fun(X2758,X2757),fun(fun(X2758,bool),bool),inj_on(X2758,X2757),X2759),X2761))
        | hBOOL(hAPP(fun(X2758,bool),bool,hAPP(X2758,fun(fun(X2758,bool),bool),member(X2758),esk71_5(X2757,X2758,X2759,X2760,X2761)),X2761)) )
      & ( ~ hBOOL(hAPP(fun(X2758,bool),bool,hAPP(fun(X2758,X2757),fun(fun(X2758,bool),bool),inj_on(X2758,X2757),X2759),X2761))
        | hBOOL(hAPP(fun(X2758,bool),bool,hAPP(fun(X2758,X2757),fun(fun(X2758,bool),bool),inj_on(X2758,X2757),X2760),X2761))
        | hAPP(X2758,X2757,X2759,esk71_5(X2757,X2758,X2759,X2760,X2761)) != hAPP(X2758,X2757,X2760,esk71_5(X2757,X2758,X2759,X2760,X2761)) )
      & ( ~ hBOOL(hAPP(fun(X2758,bool),bool,hAPP(fun(X2758,X2757),fun(fun(X2758,bool),bool),inj_on(X2758,X2757),X2760),X2761))
        | hBOOL(hAPP(fun(X2758,bool),bool,hAPP(fun(X2758,X2757),fun(fun(X2758,bool),bool),inj_on(X2758,X2757),X2759),X2761))
        | hAPP(X2758,X2757,X2759,esk71_5(X2757,X2758,X2759,X2760,X2761)) != hAPP(X2758,X2757,X2760,esk71_5(X2757,X2758,X2759,X2760,X2761)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_276_inj__on__cong])])])]) ).

cnf(i_0_976,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X4),X2)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_640]) ).

cnf(i_0_977,plain,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X4),X2)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_641]) ).

fof(i_0_978,plain,
    ! [X2237,X2238,X2239,X2240,X2241] :
      ( ( ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2237),X2238))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2239),arrow_1111136790e_Prof))
        | hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2237,X2239) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2239,X2238) )
      & ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk32_2(X2240,X2241)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2240),X2241)) )
      & ( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2240,esk32_2(X2240,X2241)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk32_2(X2240,X2241),X2241)
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2240),X2241)) ) ),
    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_142_dictator__def])])])])])]) ).

fof(i_0_979,plain,
    ! [X2358,X2359,X2360,X2361,X2362] :
      ( ~ ordere779506340up_add(X2358)
      | ~ hBOOL(hAPP(X2358,bool,hAPP(X2358,fun(X2358,bool),ord_less_eq(X2358),X2361),X2362))
      | ~ hBOOL(hAPP(X2358,bool,hAPP(X2358,fun(X2358,bool),ord_less_eq(X2358),X2359),X2360))
      | hBOOL(hAPP(X2358,bool,hAPP(X2358,fun(X2358,bool),ord_less_eq(X2358),hAPP(X2358,X2358,hAPP(X2358,fun(X2358,X2358),plus_plus(X2358),X2361),X2359)),hAPP(X2358,X2358,hAPP(X2358,fun(X2358,X2358),plus_plus(X2358),X2362),X2360))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_170_add__mono])])]) ).

fof(i_0_980,plain,
    ! [X2277,X2278,X2279,X2280,X2281] :
      ( ~ ordere223160158up_add(X2277)
      | ~ hBOOL(hAPP(X2277,bool,hAPP(X2277,fun(X2277,bool),ord_less(X2277),X2280),X2281))
      | ~ hBOOL(hAPP(X2277,bool,hAPP(X2277,fun(X2277,bool),ord_less_eq(X2277),X2278),X2279))
      | hBOOL(hAPP(X2277,bool,hAPP(X2277,fun(X2277,bool),ord_less(X2277),hAPP(X2277,X2277,hAPP(X2277,fun(X2277,X2277),plus_plus(X2277),X2280),X2278)),hAPP(X2277,X2277,hAPP(X2277,fun(X2277,X2277),plus_plus(X2277),X2281),X2279))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_150_add__less__le__mono])])]) ).

fof(i_0_981,plain,
    ! [X2282,X2283,X2284,X2285,X2286] :
      ( ~ ordere223160158up_add(X2282)
      | ~ hBOOL(hAPP(X2282,bool,hAPP(X2282,fun(X2282,bool),ord_less_eq(X2282),X2285),X2286))
      | ~ hBOOL(hAPP(X2282,bool,hAPP(X2282,fun(X2282,bool),ord_less(X2282),X2283),X2284))
      | hBOOL(hAPP(X2282,bool,hAPP(X2282,fun(X2282,bool),ord_less(X2282),hAPP(X2282,X2282,hAPP(X2282,fun(X2282,X2282),plus_plus(X2282),X2285),X2283)),hAPP(X2282,X2282,hAPP(X2282,fun(X2282,X2282),plus_plus(X2282),X2286),X2284))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_151_add__le__less__mono])])]) ).

fof(i_0_982,plain,
    ! [X2387,X2388,X2389,X2390,X2391] :
      ( ~ ordere223160158up_add(X2387)
      | ~ hBOOL(hAPP(X2387,bool,hAPP(X2387,fun(X2387,bool),ord_less(X2387),X2390),X2391))
      | ~ hBOOL(hAPP(X2387,bool,hAPP(X2387,fun(X2387,bool),ord_less(X2387),X2388),X2389))
      | hBOOL(hAPP(X2387,bool,hAPP(X2387,fun(X2387,bool),ord_less(X2387),hAPP(X2387,X2387,hAPP(X2387,fun(X2387,X2387),plus_plus(X2387),X2390),X2388)),hAPP(X2387,X2387,hAPP(X2387,fun(X2387,X2387),plus_plus(X2387),X2391),X2389))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_177_add__strict__mono])])]) ).

fof(i_0_983,plain,
    ! [X2702,X2703,X2704] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk63_3(X2702,X2703,X2704)),esk64_3(X2702,X2703,X2704)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2702),X2703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2704,X2702)),hAPP(nat,nat,X2704,X2703))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2704,esk63_3(X2702,X2703,X2704))),hAPP(nat,nat,X2704,esk64_3(X2702,X2703,X2704))))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2702),X2703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2704,X2702)),hAPP(nat,nat,X2704,X2703))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_263_less__mono__imp__le__mono])])])]) ).

fof(i_0_984,plain,
    ! [X2693,X2694,X2695,X2696] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2695),X2696))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2693),X2694))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2695),X2693)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2696),X2694))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_261_add__le__mono])]) ).

fof(i_0_985,plain,
    ! [X2650,X2651,X2652,X2653] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2652),X2653))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2650),X2651))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2652),X2650)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2653),X2651))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_246_add__less__mono])]) ).

cnf(i_0_986,plain,
    ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3)),X4)) = ti(fun(X2,bool),X4)
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),top_top(fun(X1,bool))) != top_top(fun(X2,bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_645]) ).

cnf(i_0_987,plain,
    ( hAPP(X3,X1,X4,hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X5),X4),X2)) = ti(X1,X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_646]) ).

fof(i_0_988,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    inference(fof_simplification,[status(thm)],[fact_40__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).

fof(i_0_989,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    inference(fof_simplification,[status(thm)],[fact_39__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).

fof(i_0_990,plain,
    ! [X2933,X2934] :
      ( ( ~ hBOOL(hAPP(X2933,bool,hAPP(X2933,fun(X2933,bool),ord_less_eq(X2933),hAPP(X2933,X2933,hAPP(X2933,fun(X2933,X2933),plus_plus(X2933),X2934),X2934)),zero_zero(X2933)))
        | hBOOL(hAPP(X2933,bool,hAPP(X2933,fun(X2933,bool),ord_less_eq(X2933),X2934),zero_zero(X2933)))
        | ~ linord219039673up_add(X2933) )
      & ( ~ hBOOL(hAPP(X2933,bool,hAPP(X2933,fun(X2933,bool),ord_less_eq(X2933),X2934),zero_zero(X2933)))
        | hBOOL(hAPP(X2933,bool,hAPP(X2933,fun(X2933,bool),ord_less_eq(X2933),hAPP(X2933,X2933,hAPP(X2933,fun(X2933,X2933),plus_plus(X2933),X2934),X2934)),zero_zero(X2933)))
        | ~ linord219039673up_add(X2933) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_344_double__add__le__zero__iff__single__add__le__zero])])])]) ).

fof(i_0_991,plain,
    ! [X2947,X2948] :
      ( ( ~ hBOOL(hAPP(X2947,bool,hAPP(X2947,fun(X2947,bool),ord_less(X2947),hAPP(X2947,X2947,hAPP(X2947,fun(X2947,X2947),plus_plus(X2947),X2948),X2948)),zero_zero(X2947)))
        | hBOOL(hAPP(X2947,bool,hAPP(X2947,fun(X2947,bool),ord_less(X2947),X2948),zero_zero(X2947)))
        | ~ linord219039673up_add(X2947) )
      & ( ~ hBOOL(hAPP(X2947,bool,hAPP(X2947,fun(X2947,bool),ord_less(X2947),X2948),zero_zero(X2947)))
        | hBOOL(hAPP(X2947,bool,hAPP(X2947,fun(X2947,bool),ord_less(X2947),hAPP(X2947,X2947,hAPP(X2947,fun(X2947,X2947),plus_plus(X2947),X2948),X2948)),zero_zero(X2947)))
        | ~ linord219039673up_add(X2947) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_349_double__add__less__zero__iff__single__add__less__zero])])])]) ).

fof(i_0_992,plain,
    ! [X2997,X2998] :
      ( ( ~ hBOOL(hAPP(X2997,bool,hAPP(X2997,fun(X2997,bool),ord_less(X2997),hAPP(X2997,X2997,hAPP(X2997,fun(X2997,X2997),plus_plus(X2997),X2998),X2998)),zero_zero(X2997)))
        | hBOOL(hAPP(X2997,bool,hAPP(X2997,fun(X2997,bool),ord_less(X2997),X2998),zero_zero(X2997)))
        | ~ linordered_idom(X2997) )
      & ( ~ hBOOL(hAPP(X2997,bool,hAPP(X2997,fun(X2997,bool),ord_less(X2997),X2998),zero_zero(X2997)))
        | hBOOL(hAPP(X2997,bool,hAPP(X2997,fun(X2997,bool),ord_less(X2997),hAPP(X2997,X2997,hAPP(X2997,fun(X2997,X2997),plus_plus(X2997),X2998),X2998)),zero_zero(X2997)))
        | ~ linordered_idom(X2997) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_370_even__less__0__iff])])])]) ).

cnf(i_0_993,plain,
    ( ti(fun(X1,bool),X2) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk102_5(X1,X3,X2,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_647]) ).

fof(i_0_994,plain,
    ! [X3253,X3254,X3255] :
      ( ~ ring_1(X3253)
      | ~ hBOOL(hAPP(fun(X3253,bool),bool,hAPP(X3253,fun(fun(X3253,bool),bool),member(X3253),X3255),ring_1_Ints(X3253)))
      | ~ hBOOL(hAPP(fun(X3253,bool),bool,hAPP(X3253,fun(fun(X3253,bool),bool),member(X3253),X3254),ring_1_Ints(X3253)))
      | hBOOL(hAPP(fun(X3253,bool),bool,hAPP(X3253,fun(fun(X3253,bool),bool),member(X3253),hAPP(X3253,X3253,hAPP(X3253,fun(X3253,X3253),plus_plus(X3253),X3255),X3254)),ring_1_Ints(X3253))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_476_Ints__add])])]) ).

fof(i_0_995,plain,
    ! [X2771,X2772,X2773] :
      ( ~ hBOOL(hAPP(fun(X2771,bool),bool,finite_finite_1(X2771),X2773))
      | ~ hBOOL(hAPP(fun(X2771,bool),bool,hAPP(fun(X2771,bool),fun(fun(X2771,bool),bool),ord_less_eq(fun(X2771,bool)),X2772),X2773))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X2771,bool),nat,finite_card(X2771),X2772)),hAPP(fun(X2771,bool),nat,finite_card(X2771),X2773)))
      | hBOOL(hAPP(fun(X2771,bool),bool,hAPP(fun(X2771,bool),fun(fun(X2771,bool),bool),ord_less(fun(X2771,bool)),X2772),X2773)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_280_card__psubset])]) ).

fof(i_0_996,plain,
    ! [X2583,X2584,X2585] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2583),X2585))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2583),X2584)),X2585)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2584),X2585))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2583),X2584)),X2585)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_648])])]) ).

fof(i_0_997,plain,
    ! [X2586,X2587,X2588] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2586),X2587)),X2588))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2586),X2588)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_219_add__leD1])]) ).

fof(i_0_998,plain,
    ! [X2589,X2590,X2591] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2589),X2590)),X2591))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2590),X2591)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_220_add__leD2])]) ).

fof(i_0_999,plain,
    ! [X2658,X2659,X2660] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2658),X2659)),X2660))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2658),X2660)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_248_add__lessD1])]) ).

fof(i_0_1000,plain,
    ! [X2367,X2368,X2369,X2370] :
      ( ~ ordere779506340up_add(X2367)
      | ~ hBOOL(hAPP(X2367,bool,hAPP(X2367,fun(X2367,bool),ord_less_eq(X2367),X2369),X2370))
      | hBOOL(hAPP(X2367,bool,hAPP(X2367,fun(X2367,bool),ord_less_eq(X2367),hAPP(X2367,X2367,hAPP(X2367,fun(X2367,X2367),plus_plus(X2367),X2369),X2368)),hAPP(X2367,X2367,hAPP(X2367,fun(X2367,X2367),plus_plus(X2367),X2370),X2368))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_172_add__right__mono])])]) ).

fof(i_0_1001,plain,
    ! [X2363,X2364,X2365,X2366] :
      ( ~ ordere779506340up_add(X2363)
      | ~ hBOOL(hAPP(X2363,bool,hAPP(X2363,fun(X2363,bool),ord_less_eq(X2363),X2365),X2366))
      | hBOOL(hAPP(X2363,bool,hAPP(X2363,fun(X2363,bool),ord_less_eq(X2363),hAPP(X2363,X2363,hAPP(X2363,fun(X2363,X2363),plus_plus(X2363),X2364),X2365)),hAPP(X2363,X2363,hAPP(X2363,fun(X2363,X2363),plus_plus(X2363),X2364),X2366))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_171_add__left__mono])])]) ).

fof(i_0_1002,plain,
    ! [X2396,X2397,X2398,X2399] :
      ( ~ ordere223160158up_add(X2396)
      | ~ hBOOL(hAPP(X2396,bool,hAPP(X2396,fun(X2396,bool),ord_less(X2396),X2398),X2399))
      | hBOOL(hAPP(X2396,bool,hAPP(X2396,fun(X2396,bool),ord_less(X2396),hAPP(X2396,X2396,hAPP(X2396,fun(X2396,X2396),plus_plus(X2396),X2398),X2397)),hAPP(X2396,X2396,hAPP(X2396,fun(X2396,X2396),plus_plus(X2396),X2399),X2397))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_179_add__strict__right__mono])])]) ).

fof(i_0_1003,plain,
    ! [X2392,X2393,X2394,X2395] :
      ( ~ ordere223160158up_add(X2392)
      | ~ hBOOL(hAPP(X2392,bool,hAPP(X2392,fun(X2392,bool),ord_less(X2392),X2394),X2395))
      | hBOOL(hAPP(X2392,bool,hAPP(X2392,fun(X2392,bool),ord_less(X2392),hAPP(X2392,X2392,hAPP(X2392,fun(X2392,X2392),plus_plus(X2392),X2393),X2394)),hAPP(X2392,X2392,hAPP(X2392,fun(X2392,X2392),plus_plus(X2392),X2393),X2395))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_178_add__strict__left__mono])])]) ).

fof(i_0_1004,plain,
    ! [X2690,X2691,X2692] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2691),X2692))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2691),X2690)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2692),X2690))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_260_add__le__mono1])]) ).

fof(i_0_1005,plain,
    ! [X2647,X2648,X2649] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2648),X2649))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2648),X2647)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2649),X2647))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_245_add__less__mono1])]) ).

fof(i_0_1006,plain,
    ! [X3218,X3219,X3220] :
      ( ~ hBOOL(hAPP(fun(X3218,bool),bool,finite_finite_1(X3218),X3220))
      | ~ hBOOL(hAPP(fun(X3218,bool),bool,hAPP(fun(X3218,bool),fun(fun(X3218,bool),bool),ord_less_eq(fun(X3218,bool)),X3220),hAPP(fun(X3218,bool),fun(X3218,bool),hAPP(fun(X3218,X3218),fun(fun(X3218,bool),fun(X3218,bool)),image(X3218,X3218),X3219),X3220)))
      | hBOOL(hAPP(fun(X3218,bool),bool,hAPP(fun(X3218,X3218),fun(fun(X3218,bool),bool),inj_on(X3218,X3218),X3219),X3220)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_464_finite__surj__inj])]) ).

fof(i_0_1007,plain,
    ! [X2916,X2917,X2918] :
      ( ~ ordere216010020id_add(X2916)
      | ~ hBOOL(hAPP(X2916,bool,hAPP(X2916,fun(X2916,bool),ord_less_eq(X2916),X2918),zero_zero(X2916)))
      | ~ hBOOL(hAPP(X2916,bool,hAPP(X2916,fun(X2916,bool),ord_less_eq(X2916),X2917),zero_zero(X2916)))
      | hBOOL(hAPP(X2916,bool,hAPP(X2916,fun(X2916,bool),ord_less_eq(X2916),hAPP(X2916,X2916,hAPP(X2916,fun(X2916,X2916),plus_plus(X2916),X2918),X2917)),zero_zero(X2916))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_339_add__nonpos__nonpos])])]) ).

fof(i_0_1008,plain,
    ! [X2962,X2963,X2964] :
      ( ~ ordere216010020id_add(X2962)
      | ~ hBOOL(hAPP(X2962,bool,hAPP(X2962,fun(X2962,bool),ord_less(X2962),X2964),zero_zero(X2962)))
      | ~ hBOOL(hAPP(X2962,bool,hAPP(X2962,fun(X2962,bool),ord_less_eq(X2962),X2963),zero_zero(X2962)))
      | hBOOL(hAPP(X2962,bool,hAPP(X2962,fun(X2962,bool),ord_less(X2962),hAPP(X2962,X2962,hAPP(X2962,fun(X2962,X2962),plus_plus(X2962),X2964),X2963)),zero_zero(X2962))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_358_add__neg__nonpos])])]) ).

fof(i_0_1009,plain,
    ! [X2959,X2960,X2961] :
      ( ~ ordere216010020id_add(X2959)
      | ~ hBOOL(hAPP(X2959,bool,hAPP(X2959,fun(X2959,bool),ord_less_eq(X2959),X2961),zero_zero(X2959)))
      | ~ hBOOL(hAPP(X2959,bool,hAPP(X2959,fun(X2959,bool),ord_less(X2959),X2960),zero_zero(X2959)))
      | hBOOL(hAPP(X2959,bool,hAPP(X2959,fun(X2959,bool),ord_less(X2959),hAPP(X2959,X2959,hAPP(X2959,fun(X2959,X2959),plus_plus(X2959),X2961),X2960)),zero_zero(X2959))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_357_add__nonpos__neg])])]) ).

fof(i_0_1010,plain,
    ! [X2937,X2938,X2939] :
      ( ~ ordere216010020id_add(X2937)
      | ~ hBOOL(hAPP(X2937,bool,hAPP(X2937,fun(X2937,bool),ord_less(X2937),X2939),zero_zero(X2937)))
      | ~ hBOOL(hAPP(X2937,bool,hAPP(X2937,fun(X2937,bool),ord_less(X2937),X2938),zero_zero(X2937)))
      | hBOOL(hAPP(X2937,bool,hAPP(X2937,fun(X2937,bool),ord_less(X2937),hAPP(X2937,X2937,hAPP(X2937,fun(X2937,X2937),plus_plus(X2937),X2939),X2938)),zero_zero(X2937))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_346_add__neg__neg])])]) ).

cnf(i_0_1011,plain,
    ( ti(X1,X2) = hAPP(X3,X1,X4,esk101_5(X1,X3,X2,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_649]) ).

cnf(i_0_1012,plain,
    ( ti(fun(X1,bool),X3) = ti(fun(X1,bool),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_650]) ).

fof(i_0_1013,plain,
    ! [X2235,X2236] : hBOOL(hAPP(fun(fun(X2235,X2235),bool),bool,hAPP(fun(X2235,X2235),fun(fun(fun(X2235,X2235),bool),bool),member(fun(X2235,X2235)),combi(X2235)),hAPP(fun(X2235,fun(X2235,bool)),fun(fun(X2235,X2235),bool),hAPP(fun(X2235,bool),fun(fun(X2235,fun(X2235,bool)),fun(fun(X2235,X2235),bool)),pi(X2235,X2235),X2236),hAPP(fun(X2235,bool),fun(X2235,fun(X2235,bool)),combk(fun(X2235,bool),X2235),X2236)))),
    inference(variable_rename,[status(thm)],[fact_141_funcset__id]) ).

fof(i_0_1014,plain,
    ! [X2634,X2635] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2634),X2635)),X2634)),
    inference(variable_rename,[status(thm)],[i_0_651]) ).

fof(i_0_1015,plain,
    ! [X2636,X2637] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2636),X2637)),X2637)),
    inference(variable_rename,[status(thm)],[i_0_652]) ).

cnf(i_0_1016,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,bool),fun(fun(X4,bool),bool),ord_less_eq(fun(X4,bool)),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X4,bool),X5) != hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_647]) ).

fof(i_0_1017,plain,
    ! [X3191,X3192] :
      ( ( ~ hBOOL(hAPP(fun(X3191,bool),bool,finite_finite_1(X3191),X3192))
        | hAPP(fun(X3191,bool),nat,finite_card(X3191),X3192) = hAPP(fun(X3191,bool),nat,hAPP(nat,fun(fun(X3191,bool),nat),hAPP(fun(X3191,nat),fun(nat,fun(fun(X3191,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3191,nat),fun(nat,fun(fun(X3191,bool),nat))),finite_fold_image(nat,X3191),plus_plus(nat)),hAPP(nat,fun(X3191,nat),combk(nat,X3191),one_one(nat))),zero_zero(nat)),X3192) )
      & ( hBOOL(hAPP(fun(X3191,bool),bool,finite_finite_1(X3191),X3192))
        | hAPP(fun(X3191,bool),nat,finite_card(X3191),X3192) = zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_653])]) ).

fof(i_0_1018,plain,
    ! [X3189,X3190] :
      ( ~ hBOOL(hAPP(fun(X3189,bool),bool,finite_finite_1(X3189),X3190))
      | hAPP(fun(X3189,bool),nat,finite_card(X3189),X3190) = hAPP(fun(X3189,bool),nat,hAPP(nat,fun(fun(X3189,bool),nat),hAPP(fun(X3189,nat),fun(nat,fun(fun(X3189,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3189,nat),fun(nat,fun(fun(X3189,bool),nat))),finite_fold_image(nat,X3189),plus_plus(nat)),hAPP(nat,fun(X3189,nat),combk(nat,X3189),one_one(nat))),zero_zero(nat)),X3190) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_454_card_Oeq__fold__g])]) ).

fof(i_0_1019,plain,
    ! [X2632,X2633] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X2632)),X2633)),
    inference(variable_rename,[status(thm)],[fact_239_inj__on__add__nat]) ).

fof(i_0_1020,plain,
    ! [X2784] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X2784)))),
    inference(variable_rename,[status(thm)],[fact_285_finite__Collect__le__nat]) ).

fof(i_0_1021,plain,
    ! [X2783] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2783)))),
    inference(variable_rename,[status(thm)],[fact_284_finite__Collect__less__nat]) ).

fof(i_0_1022,plain,
    ! [X3125,X3126,X3127,X3128,X3129] :
      ( ~ comm_semiring_1(X3125)
      | hAPP(X3125,X3125,hAPP(X3125,fun(X3125,X3125),plus_plus(X3125),hAPP(X3125,X3125,hAPP(X3125,fun(X3125,X3125),plus_plus(X3125),X3126),X3127)),hAPP(X3125,X3125,hAPP(X3125,fun(X3125,X3125),plus_plus(X3125),X3128),X3129)) = hAPP(X3125,X3125,hAPP(X3125,fun(X3125,X3125),plus_plus(X3125),hAPP(X3125,X3125,hAPP(X3125,fun(X3125,X3125),plus_plus(X3125),X3126),X3128)),hAPP(X3125,X3125,hAPP(X3125,fun(X3125,X3125),plus_plus(X3125),X3127),X3129)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])])]) ).

fof(i_0_1023,plain,
    ! [X3278,X3279,X3280,X3281,X3282] :
      ( ~ hBOOL(hAPP(fun(X3279,bool),bool,hAPP(X3279,fun(fun(X3279,bool),bool),member(X3279),X3281),X3282))
      | hBOOL(hAPP(fun(X3278,bool),bool,hAPP(X3278,fun(fun(X3278,bool),bool),member(X3278),hAPP(X3279,X3278,X3280,X3281)),hAPP(fun(X3279,bool),fun(X3278,bool),hAPP(fun(X3279,X3278),fun(fun(X3279,bool),fun(X3278,bool)),image(X3279,X3278),X3280),X3282))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_481_imageI])]) ).

fof(i_0_1024,plain,
    ! [X2955,X2956] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2955),X2956)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2955))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2956)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2955))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2955),X2956))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2956))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2955),X2956))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_355_add__gr__0])])]) ).

fof(i_0_1025,plain,
    ! [X2836,X2837,X2838,X2839] :
      ( ( hBOOL(hAPP(fun(X2836,bool),bool,finite_finite_1(X2836),X2838))
        | ~ hBOOL(hAPP(fun(sum_sum(X2836,X2837),bool),bool,finite_finite_1(sum_sum(X2836,X2837)),hAPP(fun(X2837,bool),fun(sum_sum(X2836,X2837),bool),hAPP(fun(X2836,bool),fun(fun(X2837,bool),fun(sum_sum(X2836,X2837),bool)),sum_Plus(X2836,X2837),X2838),X2839))) )
      & ( hBOOL(hAPP(fun(X2837,bool),bool,finite_finite_1(X2837),X2839))
        | ~ hBOOL(hAPP(fun(sum_sum(X2836,X2837),bool),bool,finite_finite_1(sum_sum(X2836,X2837)),hAPP(fun(X2837,bool),fun(sum_sum(X2836,X2837),bool),hAPP(fun(X2836,bool),fun(fun(X2837,bool),fun(sum_sum(X2836,X2837),bool)),sum_Plus(X2836,X2837),X2838),X2839))) )
      & ( ~ hBOOL(hAPP(fun(X2836,bool),bool,finite_finite_1(X2836),X2838))
        | ~ hBOOL(hAPP(fun(X2837,bool),bool,finite_finite_1(X2837),X2839))
        | hBOOL(hAPP(fun(sum_sum(X2836,X2837),bool),bool,finite_finite_1(sum_sum(X2836,X2837)),hAPP(fun(X2837,bool),fun(sum_sum(X2836,X2837),bool),hAPP(fun(X2836,bool),fun(fun(X2837,bool),fun(sum_sum(X2836,X2837),bool)),sum_Plus(X2836,X2837),X2838),X2839))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_306_finite__Plus__iff])])]) ).

fof(i_0_1026,plain,
    ! [X2844,X2845,X2846,X2847] :
      ( ~ hBOOL(hAPP(fun(sum_sum(X2844,X2845),bool),bool,finite_finite_1(sum_sum(X2844,X2845)),hAPP(fun(X2845,bool),fun(sum_sum(X2844,X2845),bool),hAPP(fun(X2844,bool),fun(fun(X2845,bool),fun(sum_sum(X2844,X2845),bool)),sum_Plus(X2844,X2845),X2846),X2847)))
      | hBOOL(hAPP(fun(X2844,bool),bool,finite_finite_1(X2844),X2846)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_308_finite__PlusD_I1_J])]) ).

fof(i_0_1027,plain,
    ! [X2848,X2849,X2850,X2851] :
      ( ~ hBOOL(hAPP(fun(sum_sum(X2848,X2849),bool),bool,finite_finite_1(sum_sum(X2848,X2849)),hAPP(fun(X2849,bool),fun(sum_sum(X2848,X2849),bool),hAPP(fun(X2848,bool),fun(fun(X2849,bool),fun(sum_sum(X2848,X2849),bool)),sum_Plus(X2848,X2849),X2850),X2851)))
      | hBOOL(hAPP(fun(X2849,bool),bool,finite_finite_1(X2849),X2851)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_309_finite__PlusD_I2_J])]) ).

cnf(i_0_1028,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),esk26_2(X1,X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_654]) ).

fof(i_0_1029,plain,
    ! [X2530,X2531,X2532,X2533] :
      ( ( hBOOL(hAPP(X2530,bool,hAPP(X2531,fun(X2530,bool),X2533,esk50_4(X2530,X2531,X2532,X2533)),esk51_4(X2530,X2531,X2532,X2533)))
        | hBOOL(hAPP(fun(X2531,fun(X2530,bool)),bool,hAPP(fun(X2531,fun(X2530,bool)),fun(fun(X2531,fun(X2530,bool)),bool),ord_less_eq(fun(X2531,fun(X2530,bool))),X2533),X2532)) )
      & ( ~ hBOOL(hAPP(X2530,bool,hAPP(X2531,fun(X2530,bool),X2532,esk50_4(X2530,X2531,X2532,X2533)),esk51_4(X2530,X2531,X2532,X2533)))
        | hBOOL(hAPP(fun(X2531,fun(X2530,bool)),bool,hAPP(fun(X2531,fun(X2530,bool)),fun(fun(X2531,fun(X2530,bool)),bool),ord_less_eq(fun(X2531,fun(X2530,bool))),X2533),X2532)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_209_predicate2I])])])]) ).

cnf(i_0_1030,plain,
    ( hAPP(X1,X4,X5,X2) = hAPP(X1,X4,X5,X3)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_655]) ).

cnf(i_0_1031,plain,
    ( ti(X1,X4) = ti(X1,X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_655]) ).

cnf(i_0_1032,plain,
    ( ti(X1,X5) = ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_656]) ).

cnf(i_0_1033,plain,
    ( ti(X1,X5) = ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_657]) ).

cnf(i_0_1034,plain,
    ( ti(X1,X5) = ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_658]) ).

cnf(i_0_1035,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)))
    | ti(X1,X2) != hAPP(X3,X1,X4,X5)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_659]) ).

cnf(i_0_1036,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ti(X4,X5) != hAPP(X1,X4,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_649]) ).

cnf(i_0_1037,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ti(X4,X5) != hAPP(X1,X4,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_660]) ).

fof(i_0_1038,plain,
    ! [X2930,X2931,X2932] :
      ( ~ ordere216010020id_add(X2930)
      | ~ hBOOL(hAPP(X2930,bool,hAPP(X2930,fun(X2930,bool),ord_less_eq(X2930),zero_zero(X2930)),X2932))
      | ~ hBOOL(hAPP(X2930,bool,hAPP(X2930,fun(X2930,bool),ord_less_eq(X2930),zero_zero(X2930)),X2931))
      | hBOOL(hAPP(X2930,bool,hAPP(X2930,fun(X2930,bool),ord_less_eq(X2930),zero_zero(X2930)),hAPP(X2930,X2930,hAPP(X2930,fun(X2930,X2930),plus_plus(X2930),X2932),X2931))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_343_add__nonneg__nonneg])])]) ).

fof(i_0_1039,plain,
    ! [X2976,X2977,X2978] :
      ( ~ ordere216010020id_add(X2976)
      | ~ hBOOL(hAPP(X2976,bool,hAPP(X2976,fun(X2976,bool),ord_less(X2976),zero_zero(X2976)),X2978))
      | ~ hBOOL(hAPP(X2976,bool,hAPP(X2976,fun(X2976,bool),ord_less_eq(X2976),zero_zero(X2976)),X2977))
      | hBOOL(hAPP(X2976,bool,hAPP(X2976,fun(X2976,bool),ord_less(X2976),zero_zero(X2976)),hAPP(X2976,X2976,hAPP(X2976,fun(X2976,X2976),plus_plus(X2976),X2978),X2977))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_362_add__pos__nonneg])])]) ).

fof(i_0_1040,plain,
    ! [X2973,X2974,X2975] :
      ( ~ ordere216010020id_add(X2973)
      | ~ hBOOL(hAPP(X2973,bool,hAPP(X2973,fun(X2973,bool),ord_less_eq(X2973),zero_zero(X2973)),X2975))
      | ~ hBOOL(hAPP(X2973,bool,hAPP(X2973,fun(X2973,bool),ord_less(X2973),zero_zero(X2973)),X2974))
      | hBOOL(hAPP(X2973,bool,hAPP(X2973,fun(X2973,bool),ord_less(X2973),zero_zero(X2973)),hAPP(X2973,X2973,hAPP(X2973,fun(X2973,X2973),plus_plus(X2973),X2975),X2974))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_361_add__nonneg__pos])])]) ).

fof(i_0_1041,plain,
    ! [X2944,X2945,X2946] :
      ( ~ ordere216010020id_add(X2944)
      | ~ hBOOL(hAPP(X2944,bool,hAPP(X2944,fun(X2944,bool),ord_less(X2944),zero_zero(X2944)),X2946))
      | ~ hBOOL(hAPP(X2944,bool,hAPP(X2944,fun(X2944,bool),ord_less(X2944),zero_zero(X2944)),X2945))
      | hBOOL(hAPP(X2944,bool,hAPP(X2944,fun(X2944,bool),ord_less(X2944),zero_zero(X2944)),hAPP(X2944,X2944,hAPP(X2944,fun(X2944,X2944),plus_plus(X2944),X2946),X2945))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_348_add__pos__pos])])]) ).

fof(i_0_1042,plain,
    ! [X3335,X3336,X3337,X3338,X3339] : hAPP(fun(X3335,bool),fun(X3336,bool),hAPP(fun(X3335,X3336),fun(fun(X3335,bool),fun(X3336,bool)),image(X3335,X3336),hAPP(fun(X3335,X3337),fun(X3335,X3336),hAPP(fun(X3337,X3336),fun(fun(X3335,X3337),fun(X3335,X3336)),combb(X3337,X3336,X3335),X3338),X3339)),top_top(fun(X3335,bool))) = hAPP(fun(X3337,bool),fun(X3336,bool),hAPP(fun(X3337,X3336),fun(fun(X3337,bool),fun(X3336,bool)),image(X3337,X3336),X3338),hAPP(fun(X3335,bool),fun(X3337,bool),hAPP(fun(X3335,X3337),fun(fun(X3335,bool),fun(X3337,bool)),image(X3335,X3337),X3339),top_top(fun(X3335,bool)))),
    inference(variable_rename,[status(thm)],[fact_490_range__composition]) ).

fof(i_0_1043,plain,
    ! [X2923,X2924,X2925,X2926] :
      ( ~ ordere216010020id_add(X2923)
      | ~ hBOOL(hAPP(X2923,bool,hAPP(X2923,fun(X2923,bool),ord_less_eq(X2923),zero_zero(X2923)),X2926))
      | ~ hBOOL(hAPP(X2923,bool,hAPP(X2923,fun(X2923,bool),ord_less_eq(X2923),X2924),X2925))
      | hBOOL(hAPP(X2923,bool,hAPP(X2923,fun(X2923,bool),ord_less_eq(X2923),X2924),hAPP(X2923,X2923,hAPP(X2923,fun(X2923,X2923),plus_plus(X2923),X2926),X2925))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_341_add__increasing])])]) ).

fof(i_0_1044,plain,
    ! [X2919,X2920,X2921,X2922] :
      ( ~ ordere216010020id_add(X2919)
      | ~ hBOOL(hAPP(X2919,bool,hAPP(X2919,fun(X2919,bool),ord_less_eq(X2919),zero_zero(X2919)),X2922))
      | ~ hBOOL(hAPP(X2919,bool,hAPP(X2919,fun(X2919,bool),ord_less_eq(X2919),X2920),X2921))
      | hBOOL(hAPP(X2919,bool,hAPP(X2919,fun(X2919,bool),ord_less_eq(X2919),X2920),hAPP(X2919,X2919,hAPP(X2919,fun(X2919,X2919),plus_plus(X2919),X2921),X2922))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_340_add__increasing2])])]) ).

fof(i_0_1045,plain,
    ! [X2969,X2970,X2971,X2972] :
      ( ~ ordere216010020id_add(X2969)
      | ~ hBOOL(hAPP(X2969,bool,hAPP(X2969,fun(X2969,bool),ord_less(X2969),zero_zero(X2969)),X2972))
      | ~ hBOOL(hAPP(X2969,bool,hAPP(X2969,fun(X2969,bool),ord_less_eq(X2969),X2970),X2971))
      | hBOOL(hAPP(X2969,bool,hAPP(X2969,fun(X2969,bool),ord_less(X2969),X2970),hAPP(X2969,X2969,hAPP(X2969,fun(X2969,X2969),plus_plus(X2969),X2972),X2971))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_360_add__strict__increasing])])]) ).

fof(i_0_1046,plain,
    ! [X2965,X2966,X2967,X2968] :
      ( ~ ordere216010020id_add(X2965)
      | ~ hBOOL(hAPP(X2965,bool,hAPP(X2965,fun(X2965,bool),ord_less_eq(X2965),zero_zero(X2965)),X2968))
      | ~ hBOOL(hAPP(X2965,bool,hAPP(X2965,fun(X2965,bool),ord_less(X2965),X2966),X2967))
      | hBOOL(hAPP(X2965,bool,hAPP(X2965,fun(X2965,bool),ord_less(X2965),X2966),hAPP(X2965,X2965,hAPP(X2965,fun(X2965,X2965),plus_plus(X2965),X2968),X2967))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_359_add__strict__increasing2])])]) ).

fof(i_0_1047,plain,
    ! [X2940,X2941,X2942,X2943] :
      ( ~ linordered_semidom(X2940)
      | ~ hBOOL(hAPP(X2940,bool,hAPP(X2940,fun(X2940,bool),ord_less(X2940),zero_zero(X2940)),X2943))
      | ~ hBOOL(hAPP(X2940,bool,hAPP(X2940,fun(X2940,bool),ord_less(X2940),X2941),X2942))
      | hBOOL(hAPP(X2940,bool,hAPP(X2940,fun(X2940,bool),ord_less(X2940),X2941),hAPP(X2940,X2940,hAPP(X2940,fun(X2940,X2940),plus_plus(X2940),X2943),X2942))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_347_pos__add__strict])])]) ).

fof(i_0_1048,plain,
    ! [X3185,X3186,X3187] :
      ( ( hBOOL(hAPP(X3185,bool,hAPP(X3185,fun(X3185,bool),ord_less(X3185),zero_zero(X3185)),esk99_3(X3185,X3186,X3187)))
        | hBOOL(hAPP(X3185,bool,hAPP(X3185,fun(X3185,bool),ord_less_eq(X3185),X3186),X3187))
        | ~ linordered_field(X3185) )
      & ( ~ hBOOL(hAPP(X3185,bool,hAPP(X3185,fun(X3185,bool),ord_less_eq(X3185),X3186),hAPP(X3185,X3185,hAPP(X3185,fun(X3185,X3185),plus_plus(X3185),X3187),esk99_3(X3185,X3186,X3187))))
        | hBOOL(hAPP(X3185,bool,hAPP(X3185,fun(X3185,bool),ord_less_eq(X3185),X3186),X3187))
        | ~ linordered_field(X3185) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_453_field__le__epsilon])])])])]) ).

fof(i_0_1049,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),esk19_0))
    & hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk19_0),arrow_2064824852le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_661])])]) ).

fof(i_0_1050,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),esk18_0))
    & hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk18_0),arrow_2064824852le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_662])])]) ).

fof(i_0_1051,plain,
    ! [X3295,X3296,X3297,X3298,X3299,X3300] : hAPP(fun(X3295,bool),fun(X3296,bool),hAPP(fun(X3295,X3296),fun(fun(X3295,bool),fun(X3296,bool)),image(X3295,X3296),X3298),hAPP(fun(X3297,bool),fun(X3295,bool),hAPP(fun(X3297,X3295),fun(fun(X3297,bool),fun(X3295,bool)),image(X3297,X3295),X3299),X3300)) = hAPP(fun(X3297,bool),fun(X3296,bool),hAPP(fun(X3297,X3296),fun(fun(X3297,bool),fun(X3296,bool)),image(X3297,X3296),hAPP(fun(X3297,X3295),fun(X3297,X3296),hAPP(fun(X3295,X3296),fun(fun(X3297,X3295),fun(X3297,X3296)),combb(X3295,X3296,X3297),X3298),X3299)),X3300),
    inference(variable_rename,[status(thm)],[fact_483_image__image]) ).

fof(i_0_1052,plain,
    ! [X2296,X2297,X2298,X2299] :
      ( ( hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less(X2296),X2298),esk38_4(X2296,X2297,X2298,X2299)))
        | hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less_eq(X2296),X2299),X2297))
        | ~ hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less(X2296),X2298),X2299))
        | ~ dense_linorder(X2296) )
      & ( hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less(X2296),esk38_4(X2296,X2297,X2298,X2299)),X2299))
        | hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less_eq(X2296),X2299),X2297))
        | ~ hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less(X2296),X2298),X2299))
        | ~ dense_linorder(X2296) )
      & ( ~ hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less_eq(X2296),esk38_4(X2296,X2297,X2298,X2299)),X2297))
        | hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less_eq(X2296),X2299),X2297))
        | ~ hBOOL(hAPP(X2296,bool,hAPP(X2296,fun(X2296,bool),ord_less(X2296),X2298),X2299))
        | ~ dense_linorder(X2296) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_154_dense__le__bounded])])])])]) ).

cnf(i_0_1053,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X4),X3),X6) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | hAPP(X1,X2,X3,X5) != ti(X2,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_663]) ).

fof(i_0_1054,plain,
    ! [X1831,X1832,X1833,X1835,X1836,X1837,X1838,X1839,X1842] :
      ( ( ~ hBOOL(hAPP(product_prod(X1831,X1832),bool,X1833,esk6_3(X1831,X1832,X1833)))
        | hBOOL(hAPP(product_prod(X1831,X1832),bool,X1833,hAPP(X1832,product_prod(X1831,X1832),hAPP(X1831,fun(X1832,product_prod(X1831,X1832)),product_Pair(X1831,X1832),X1835),X1836))) )
      & ( ~ hBOOL(hAPP(product_prod(X1837,X1838),bool,X1839,hAPP(X1838,product_prod(X1837,X1838),hAPP(X1837,fun(X1838,product_prod(X1837,X1838)),product_Pair(X1837,X1838),esk7_3(X1837,X1838,X1839)),esk8_3(X1837,X1838,X1839))))
        | hBOOL(hAPP(product_prod(X1837,X1838),bool,X1839,X1842)) ) ),
    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])])])])]) ).

cnf(i_0_1055,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X4),X3),hAPP(X1,X2,X3,X5)) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_664]) ).

fof(i_0_1056,plain,
    ! [X2935,X2936] :
      ( ( ~ hBOOL(hAPP(X2935,bool,hAPP(X2935,fun(X2935,bool),ord_less_eq(X2935),zero_zero(X2935)),hAPP(X2935,X2935,hAPP(X2935,fun(X2935,X2935),plus_plus(X2935),X2936),X2936)))
        | hBOOL(hAPP(X2935,bool,hAPP(X2935,fun(X2935,bool),ord_less_eq(X2935),zero_zero(X2935)),X2936))
        | ~ linord219039673up_add(X2935) )
      & ( ~ hBOOL(hAPP(X2935,bool,hAPP(X2935,fun(X2935,bool),ord_less_eq(X2935),zero_zero(X2935)),X2936))
        | hBOOL(hAPP(X2935,bool,hAPP(X2935,fun(X2935,bool),ord_less_eq(X2935),zero_zero(X2935)),hAPP(X2935,X2935,hAPP(X2935,fun(X2935,X2935),plus_plus(X2935),X2936),X2936)))
        | ~ linord219039673up_add(X2935) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_345_zero__le__double__add__iff__zero__le__single__add])])])]) ).

fof(i_0_1057,plain,
    ! [X2949,X2950] :
      ( ( ~ hBOOL(hAPP(X2949,bool,hAPP(X2949,fun(X2949,bool),ord_less(X2949),zero_zero(X2949)),hAPP(X2949,X2949,hAPP(X2949,fun(X2949,X2949),plus_plus(X2949),X2950),X2950)))
        | hBOOL(hAPP(X2949,bool,hAPP(X2949,fun(X2949,bool),ord_less(X2949),zero_zero(X2949)),X2950))
        | ~ linord219039673up_add(X2949) )
      & ( ~ hBOOL(hAPP(X2949,bool,hAPP(X2949,fun(X2949,bool),ord_less(X2949),zero_zero(X2949)),X2950))
        | hBOOL(hAPP(X2949,bool,hAPP(X2949,fun(X2949,bool),ord_less(X2949),zero_zero(X2949)),hAPP(X2949,X2949,hAPP(X2949,fun(X2949,X2949),plus_plus(X2949),X2950),X2950)))
        | ~ linord219039673up_add(X2949) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_350_zero__less__double__add__iff__zero__less__single__add])])])]) ).

fof(i_0_1058,plain,
    ! [X2477,X2478,X2479,X2480,X2481,X2482] :
      ( ~ hBOOL(hAPP(X2477,bool,hAPP(X2478,fun(X2477,bool),X2480,X2481),X2482))
      | ~ hBOOL(hAPP(fun(X2478,fun(X2477,bool)),bool,hAPP(fun(X2478,fun(X2477,bool)),fun(fun(X2478,fun(X2477,bool)),bool),ord_less_eq(fun(X2478,fun(X2477,bool))),X2480),X2479))
      | hBOOL(hAPP(X2477,bool,hAPP(X2478,fun(X2477,bool),X2479,X2481),X2482)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_195_rev__predicate2D])]) ).

fof(i_0_1059,plain,
    ! [X2486,X2487,X2488,X2489,X2490,X2491] :
      ( ~ hBOOL(hAPP(fun(X2486,fun(X2487,bool)),bool,hAPP(fun(X2486,fun(X2487,bool)),fun(fun(X2486,fun(X2487,bool)),bool),ord_less_eq(fun(X2486,fun(X2487,bool))),X2490),X2491))
      | ~ hBOOL(hAPP(X2487,bool,hAPP(X2486,fun(X2487,bool),X2490,X2488),X2489))
      | hBOOL(hAPP(X2487,bool,hAPP(X2486,fun(X2487,bool),X2491,X2488),X2489)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_197_predicate2D])]) ).

fof(i_0_1060,plain,
    ! [X2777,X2778,X2779] :
      ( ~ hBOOL(hAPP(fun(X2777,bool),bool,finite_finite_1(X2777),X2779))
      | ~ hBOOL(hAPP(fun(X2777,bool),bool,hAPP(fun(X2777,bool),fun(fun(X2777,bool),bool),ord_less_eq(fun(X2777,bool)),X2778),X2779))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X2777,bool),nat,finite_card(X2777),X2778)),hAPP(fun(X2777,bool),nat,finite_card(X2777),X2779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_282_card__mono])]) ).

fof(i_0_1061,plain,
    ! [X2774,X2775,X2776] :
      ( ~ hBOOL(hAPP(fun(X2774,bool),bool,finite_finite_1(X2774),X2776))
      | ~ hBOOL(hAPP(fun(X2774,bool),bool,hAPP(fun(X2774,bool),fun(fun(X2774,bool),bool),ord_less(fun(X2774,bool)),X2775),X2776))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X2774,bool),nat,finite_card(X2774),X2775)),hAPP(fun(X2774,bool),nat,finite_card(X2774),X2776))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_281_psubset__card__mono])]) ).

cnf(i_0_1062,plain,
    ( hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3) = ti(fun(X2,X1),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,esk34_4(X1,X2,X4,X3))) != ti(X2,esk34_4(X1,X2,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_665]) ).

fof(i_0_1063,plain,
    ! [X3080,X3081] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3080),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3080),X3081)))),
    inference(variable_rename,[status(thm)],[fact_412_less__add__Suc1]) ).

fof(i_0_1064,plain,
    ! [X3078,X3079] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3078),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3079),X3078)))),
    inference(variable_rename,[status(thm)],[fact_411_less__add__Suc2]) ).

fof(i_0_1065,plain,
    ! [X2492,X2493,X2494,X2495] :
      ( ~ hBOOL(hAPP(fun(X2492,bool),bool,hAPP(fun(X2492,bool),fun(fun(X2492,bool),bool),ord_less_eq(fun(X2492,bool)),X2494),X2495))
      | ~ hBOOL(hAPP(fun(X2492,bool),bool,hAPP(fun(X2492,bool),fun(fun(X2492,bool),bool),ord_less_eq(fun(X2492,bool)),X2495),X2493))
      | hBOOL(hAPP(fun(X2492,bool),bool,hAPP(fun(X2492,bool),fun(fun(X2492,bool),bool),ord_less_eq(fun(X2492,bool)),X2494),X2493)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_198_subset__trans])]) ).

fof(i_0_1066,plain,
    ! [X2469,X2470,X2471,X2472] :
      ( ~ hBOOL(hAPP(fun(X2469,bool),bool,hAPP(fun(X2469,bool),fun(fun(X2469,bool),bool),ord_less(fun(X2469,bool)),X2471),X2472))
      | ~ hBOOL(hAPP(fun(X2469,bool),bool,hAPP(fun(X2469,bool),fun(fun(X2469,bool),bool),ord_less_eq(fun(X2469,bool)),X2472),X2470))
      | hBOOL(hAPP(fun(X2469,bool),bool,hAPP(fun(X2469,bool),fun(fun(X2469,bool),bool),ord_less(fun(X2469,bool)),X2471),X2470)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_193_psubset__subset__trans])]) ).

fof(i_0_1067,plain,
    ! [X2473,X2474,X2475,X2476] :
      ( ~ hBOOL(hAPP(fun(X2473,bool),bool,hAPP(fun(X2473,bool),fun(fun(X2473,bool),bool),ord_less_eq(fun(X2473,bool)),X2475),X2476))
      | ~ hBOOL(hAPP(fun(X2473,bool),bool,hAPP(fun(X2473,bool),fun(fun(X2473,bool),bool),ord_less(fun(X2473,bool)),X2476),X2474))
      | hBOOL(hAPP(fun(X2473,bool),bool,hAPP(fun(X2473,bool),fun(fun(X2473,bool),bool),ord_less(fun(X2473,bool)),X2475),X2474)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_194_subset__psubset__trans])]) ).

fof(i_0_1068,plain,
    ! [X2566,X2567,X2568,X2569] :
      ( ~ hBOOL(hAPP(fun(X2566,bool),bool,hAPP(fun(X2566,bool),fun(fun(X2566,bool),bool),ord_less(fun(X2566,bool)),X2568),X2569))
      | ~ hBOOL(hAPP(fun(X2566,bool),bool,hAPP(fun(X2566,bool),fun(fun(X2566,bool),bool),ord_less(fun(X2566,bool)),X2569),X2567))
      | hBOOL(hAPP(fun(X2566,bool),bool,hAPP(fun(X2566,bool),fun(fun(X2566,bool),bool),ord_less(fun(X2566,bool)),X2568),X2567)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_215_psubset__trans])]) ).

fof(i_0_1069,plain,
    ! [X3015,X3016] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3015)),hAPP(nat,nat,suc,X3016)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3015),X3016)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3015),X3016))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3015)),hAPP(nat,nat,suc,X3016))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_380_Suc__le__mono])]) ).

fof(i_0_1070,plain,
    ! [X3056,X3057] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3056)),hAPP(nat,nat,suc,X3057)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3056),X3057)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_401_Suc__less__SucD])]) ).

fof(i_0_1071,plain,
    ! [X3039,X3040] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3039)),hAPP(nat,nat,suc,X3040)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3039),X3040)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3039),X3040))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3039)),hAPP(nat,nat,suc,X3040))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_393_Suc__less__eq])]) ).

fof(i_0_1072,plain,
    ! [X3345,X3346,X3347,X3348] : hBOOL(hAPP(fun(X3345,bool),bool,hAPP(X3345,fun(fun(X3345,bool),bool),member(X3345),hAPP(X3346,X3345,X3347,X3348)),hAPP(fun(X3346,bool),fun(X3345,bool),hAPP(fun(X3346,X3345),fun(fun(X3346,bool),fun(X3345,bool)),image(X3346,X3345),X3347),top_top(fun(X3346,bool))))),
    inference(variable_rename,[status(thm)],[fact_492_rangeI]) ).

fof(i_0_1073,plain,
    ! [X2316,X2317,X2318,X2319,X2320] :
      ( ~ hBOOL(hAPP(fun(X2316,bool),bool,hAPP(fun(X2316,X2317),fun(fun(X2316,bool),bool),inj_on(X2316,X2317),X2319),X2320))
      | ~ hBOOL(hAPP(fun(X2316,bool),bool,hAPP(fun(X2316,bool),fun(fun(X2316,bool),bool),ord_less_eq(fun(X2316,bool)),X2318),X2320))
      | hBOOL(hAPP(fun(X2316,bool),bool,hAPP(fun(X2316,X2317),fun(fun(X2316,bool),bool),inj_on(X2316,X2317),X2319),X2318)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_159_subset__inj__on])]) ).

cnf(i_0_1074,plain,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X5)
    | ti(X1,X2) != ti(X1,X3)
    | ti(X1,X4) != ti(X1,X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_666]) ).

cnf(i_0_1075,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_666]) ).

cnf(i_0_1076,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_666]) ).

cnf(i_0_1077,plain,
    ( ti(X1,X2) = ti(X1,X4)
    | ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_667]) ).

cnf(i_0_1078,plain,
    ( ti(X1,X3) = ti(X1,X5)
    | ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_668]) ).

fof(i_0_1079,plain,
    ! [X3049,X3050,X3051] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3050),X3051))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3051),X3049))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3050)),X3049)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_398_less__trans__Suc])]) ).

fof(i_0_1080,plain,
    ! [X3121,X3122,X3123,X3124] :
      ( ~ comm_semiring_1(X3121)
      | hAPP(X3121,X3121,hAPP(X3121,fun(X3121,X3121),plus_plus(X3121),hAPP(X3121,X3121,hAPP(X3121,fun(X3121,X3121),plus_plus(X3121),X3122),X3123)),X3124) = hAPP(X3121,X3121,hAPP(X3121,fun(X3121,X3121),plus_plus(X3121),hAPP(X3121,X3121,hAPP(X3121,fun(X3121,X3121),plus_plus(X3121),X3122),X3124)),X3123) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])])]) ).

fof(i_0_1081,plain,
    ! [X2840,X2841,X2842,X2843] :
      ( ~ hBOOL(hAPP(fun(X2841,bool),bool,finite_finite_1(X2841),X2843))
      | ~ hBOOL(hAPP(fun(X2840,bool),bool,finite_finite_1(X2840),X2842))
      | hBOOL(hAPP(fun(sum_sum(X2841,X2840),bool),bool,finite_finite_1(sum_sum(X2841,X2840)),hAPP(fun(X2840,bool),fun(sum_sum(X2841,X2840),bool),hAPP(fun(X2841,bool),fun(fun(X2840,bool),fun(sum_sum(X2841,X2840),bool)),sum_Plus(X2841,X2840),X2843),X2842))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_307_finite__Plus])]) ).

fof(i_0_1082,plain,
    ! [X2500,X2501,X2502,X2503] :
      ( ~ hBOOL(hAPP(fun(X2500,bool),bool,hAPP(X2500,fun(fun(X2500,bool),bool),member(X2500),X2502),X2503))
      | ~ hBOOL(hAPP(fun(X2500,bool),bool,hAPP(fun(X2500,bool),fun(fun(X2500,bool),bool),ord_less_eq(fun(X2500,bool)),X2503),X2501))
      | hBOOL(hAPP(fun(X2500,bool),bool,hAPP(X2500,fun(fun(X2500,bool),bool),member(X2500),X2502),X2501)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_200_set__rev__mp])]) ).

fof(i_0_1083,plain,
    ! [X2508,X2509,X2510,X2511] :
      ( ~ hBOOL(hAPP(fun(X2508,bool),bool,hAPP(fun(X2508,bool),fun(fun(X2508,bool),bool),ord_less_eq(fun(X2508,bool)),X2510),X2511))
      | ~ hBOOL(hAPP(fun(X2508,bool),bool,hAPP(X2508,fun(fun(X2508,bool),bool),member(X2508),X2509),X2510))
      | hBOOL(hAPP(fun(X2508,bool),bool,hAPP(X2508,fun(fun(X2508,bool),bool),member(X2508),X2509),X2511)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_202_in__mono])]) ).

fof(i_0_1084,plain,
    ! [X2496,X2497,X2498,X2499] :
      ( ~ hBOOL(hAPP(fun(X2496,bool),bool,hAPP(fun(X2496,bool),fun(fun(X2496,bool),bool),ord_less_eq(fun(X2496,bool)),X2498),X2499))
      | ~ hBOOL(hAPP(fun(X2496,bool),bool,hAPP(X2496,fun(fun(X2496,bool),bool),member(X2496),X2497),X2498))
      | hBOOL(hAPP(fun(X2496,bool),bool,hAPP(X2496,fun(fun(X2496,bool),bool),member(X2496),X2497),X2499)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_199_set__mp])]) ).

fof(i_0_1085,plain,
    ! [X2456,X2457,X2458,X2459] :
      ( ~ hBOOL(hAPP(fun(X2456,bool),bool,hAPP(fun(X2456,bool),fun(fun(X2456,bool),bool),ord_less_eq(fun(X2456,bool)),X2458),X2459))
      | ~ hBOOL(hAPP(fun(X2456,bool),bool,hAPP(X2456,fun(fun(X2456,bool),bool),member(X2456),X2457),X2458))
      | hBOOL(hAPP(fun(X2456,bool),bool,hAPP(X2456,fun(fun(X2456,bool),bool),member(X2456),X2457),X2459)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_189_subsetD])]) ).

fof(i_0_1086,plain,
    ! [X2562,X2563,X2564,X2565] :
      ( ~ hBOOL(hAPP(fun(X2562,bool),bool,hAPP(fun(X2562,bool),fun(fun(X2562,bool),bool),ord_less(fun(X2562,bool)),X2564),X2565))
      | ~ hBOOL(hAPP(fun(X2562,bool),bool,hAPP(X2562,fun(fun(X2562,bool),bool),member(X2562),X2563),X2564))
      | hBOOL(hAPP(fun(X2562,bool),bool,hAPP(X2562,fun(fun(X2562,bool),bool),member(X2562),X2563),X2565)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_214_psubsetD])]) ).

fof(i_0_1087,plain,
    ! [X2096,X2097,X2098,X2099,X2100] :
      ( ~ ord(X2097)
      | ~ hBOOL(hAPP(fun(X2096,X2097),bool,hAPP(fun(X2096,X2097),fun(fun(X2096,X2097),bool),ord_less_eq(fun(X2096,X2097)),X2099),X2100))
      | hBOOL(hAPP(X2097,bool,hAPP(X2097,fun(X2097,bool),ord_less_eq(X2097),hAPP(X2096,X2097,X2099,X2098)),hAPP(X2096,X2097,X2100,X2098))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_104_le__funD])])]) ).

fof(i_0_1088,plain,
    ! [X2058,X2059,X2060,X2061,X2062] :
      ( ~ ord(X2059)
      | ~ hBOOL(hAPP(fun(X2058,X2059),bool,hAPP(fun(X2058,X2059),fun(fun(X2058,X2059),bool),ord_less_eq(fun(X2058,X2059)),X2061),X2062))
      | hBOOL(hAPP(X2059,bool,hAPP(X2059,fun(X2059,bool),ord_less_eq(X2059),hAPP(X2058,X2059,X2061,X2060)),hAPP(X2058,X2059,X2062,X2060))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_94_le__funE])])]) ).

fof(i_0_1089,plain,
    ! [X3011,X3012] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3011),X3012))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3012)),X3011)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3012)),X3011))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3011),X3012)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_669])]) ).

cnf(i_0_1090,plain,
    ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),finite908156982e_idem(X1,X2)) = finite908156982e_idem(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_670]) ).

fof(i_0_1091,plain,
    ! [X2301,X2302,X2303,X2304] :
      ( ( hBOOL(hAPP(fun(X2301,X2302),bool,hAPP(fun(X2301,X2302),fun(fun(X2301,X2302),bool),ord_less_eq(fun(X2301,X2302)),X2303),X2304))
        | ~ hBOOL(hAPP(fun(X2301,X2302),bool,hAPP(fun(X2301,X2302),fun(fun(X2301,X2302),bool),ord_less(fun(X2301,X2302)),X2303),X2304))
        | ~ ord(X2302) )
      & ( ~ hBOOL(hAPP(fun(X2301,X2302),bool,hAPP(fun(X2301,X2302),fun(fun(X2301,X2302),bool),ord_less_eq(fun(X2301,X2302)),X2304),X2303))
        | ~ hBOOL(hAPP(fun(X2301,X2302),bool,hAPP(fun(X2301,X2302),fun(fun(X2301,X2302),bool),ord_less(fun(X2301,X2302)),X2303),X2304))
        | ~ ord(X2302) )
      & ( ~ hBOOL(hAPP(fun(X2301,X2302),bool,hAPP(fun(X2301,X2302),fun(fun(X2301,X2302),bool),ord_less_eq(fun(X2301,X2302)),X2303),X2304))
        | hBOOL(hAPP(fun(X2301,X2302),bool,hAPP(fun(X2301,X2302),fun(fun(X2301,X2302),bool),ord_less_eq(fun(X2301,X2302)),X2304),X2303))
        | hBOOL(hAPP(fun(X2301,X2302),bool,hAPP(fun(X2301,X2302),fun(fun(X2301,X2302),bool),ord_less(fun(X2301,X2302)),X2303),X2304))
        | ~ ord(X2302) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_671])])])]) ).

cnf(i_0_1092,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),top_top(fun(X3,bool)))))
    | ti(X1,X2) != hAPP(X3,X1,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_672]) ).

fof(i_0_1093,plain,
    ! [X2882,X2883,X2884,X2885] :
      ( ( ~ hBOOL(hAPP(fun(X2883,bool),bool,finite_finite_1(X2883),X2885))
        | ~ hBOOL(hAPP(fun(X2882,bool),bool,finite_finite_1(X2882),X2884))
        | hAPP(fun(sum_sum(X2883,X2882),bool),nat,finite_card(sum_sum(X2883,X2882)),hAPP(fun(X2882,bool),fun(sum_sum(X2883,X2882),bool),hAPP(fun(X2883,bool),fun(fun(X2882,bool),fun(sum_sum(X2883,X2882),bool)),sum_Plus(X2883,X2882),X2885),X2884)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X2883,bool),nat,finite_card(X2883),X2885)),hAPP(fun(X2882,bool),nat,finite_card(X2882),X2884)) )
      & ( hBOOL(hAPP(fun(X2883,bool),bool,finite_finite_1(X2883),X2885))
        | hAPP(fun(sum_sum(X2883,X2882),bool),nat,finite_card(sum_sum(X2883,X2882)),hAPP(fun(X2882,bool),fun(sum_sum(X2883,X2882),bool),hAPP(fun(X2883,bool),fun(fun(X2882,bool),fun(sum_sum(X2883,X2882),bool)),sum_Plus(X2883,X2882),X2885),X2884)) = zero_zero(nat) )
      & ( hBOOL(hAPP(fun(X2882,bool),bool,finite_finite_1(X2882),X2884))
        | hAPP(fun(sum_sum(X2883,X2882),bool),nat,finite_card(sum_sum(X2883,X2882)),hAPP(fun(X2882,bool),fun(sum_sum(X2883,X2882),bool),hAPP(fun(X2883,bool),fun(fun(X2882,bool),fun(sum_sum(X2883,X2882),bool)),sum_Plus(X2883,X2882),X2885),X2884)) = zero_zero(nat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_317_card__Plus__conv__if])])]) ).

fof(i_0_1094,plain,
    ! [X2817,X2818,X2819,X2820] :
      ( ~ hBOOL(hAPP(fun(X2818,bool),bool,finite_finite_1(X2818),X2820))
      | ~ hBOOL(hAPP(fun(X2817,bool),bool,finite_finite_1(X2817),X2819))
      | hAPP(fun(sum_sum(X2818,X2817),bool),nat,finite_card(sum_sum(X2818,X2817)),hAPP(fun(X2817,bool),fun(sum_sum(X2818,X2817),bool),hAPP(fun(X2818,bool),fun(fun(X2817,bool),fun(sum_sum(X2818,X2817),bool)),sum_Plus(X2818,X2817),X2820),X2819)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X2818,bool),nat,finite_card(X2818),X2820)),hAPP(fun(X2817,bool),nat,finite_card(X2817),X2819)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_302_card__Plus])]) ).

cnf(i_0_1095,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_673]) ).

cnf(i_0_1096,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_674]) ).

fof(i_0_1097,plain,
    ! [X3237,X3238,X3239,X3240] :
      ( ~ hBOOL(hAPP(fun(X3238,bool),bool,finite_finite_1(X3238),X3240))
      | hAPP(fun(X3237,bool),nat,finite_card(X3237),hAPP(fun(X3238,bool),fun(X3237,bool),hAPP(fun(X3238,X3237),fun(fun(X3238,bool),fun(X3237,bool)),image(X3238,X3237),X3239),X3240)) != hAPP(fun(X3238,bool),nat,finite_card(X3238),X3240)
      | hBOOL(hAPP(fun(X3238,bool),bool,hAPP(fun(X3238,X3237),fun(fun(X3238,bool),bool),inj_on(X3238,X3237),X3239),X3240)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_470_eq__card__imp__inj__on])]) ).

fof(i_0_1098,plain,
    ! [X3241,X3242,X3243,X3244] :
      ( ( ~ hBOOL(hAPP(fun(X3242,bool),bool,hAPP(fun(X3242,X3241),fun(fun(X3242,bool),bool),inj_on(X3242,X3241),X3243),X3244))
        | hAPP(fun(X3241,bool),nat,finite_card(X3241),hAPP(fun(X3242,bool),fun(X3241,bool),hAPP(fun(X3242,X3241),fun(fun(X3242,bool),fun(X3241,bool)),image(X3242,X3241),X3243),X3244)) = hAPP(fun(X3242,bool),nat,finite_card(X3242),X3244)
        | ~ hBOOL(hAPP(fun(X3242,bool),bool,finite_finite_1(X3242),X3244)) )
      & ( hAPP(fun(X3241,bool),nat,finite_card(X3241),hAPP(fun(X3242,bool),fun(X3241,bool),hAPP(fun(X3242,X3241),fun(fun(X3242,bool),fun(X3241,bool)),image(X3242,X3241),X3243),X3244)) != hAPP(fun(X3242,bool),nat,finite_card(X3242),X3244)
        | hBOOL(hAPP(fun(X3242,bool),bool,hAPP(fun(X3242,X3241),fun(fun(X3242,bool),bool),inj_on(X3242,X3241),X3243),X3244))
        | ~ hBOOL(hAPP(fun(X3242,bool),bool,finite_finite_1(X3242),X3244)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_471_inj__on__iff__eq__card])])]) ).

fof(i_0_1099,plain,
    ! [X2707,X2708,X2709] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2708),X2709))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2708),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2709),X2707))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_termination__basic__simps_I3_J])]) ).

fof(i_0_1100,plain,
    ! [X2684,X2685,X2686] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2685),X2686))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2685),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2686),X2684))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_258_trans__le__add1])]) ).

fof(i_0_1101,plain,
    ! [X2710,X2711,X2712] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2711),X2712))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2711),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2710),X2712))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_265_termination__basic__simps_I4_J])]) ).

fof(i_0_1102,plain,
    ! [X2687,X2688,X2689] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2688),X2689))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2688),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2687),X2689))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_259_trans__le__add2])]) ).

fof(i_0_1103,plain,
    ! [X2716,X2717,X2718] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2717),X2718))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2717),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2718),X2716))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_267_termination__basic__simps_I1_J])]) ).

fof(i_0_1104,plain,
    ! [X2641,X2642,X2643] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2642),X2643))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2642),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2643),X2641))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_243_trans__less__add1])]) ).

fof(i_0_1105,plain,
    ! [X2713,X2714,X2715] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2714),X2715))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2714),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2713),X2715))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_266_termination__basic__simps_I2_J])]) ).

fof(i_0_1106,plain,
    ! [X2644,X2645,X2646] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2645),X2646))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2645),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2644),X2646))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_244_trans__less__add2])]) ).

cnf(i_0_1107,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3),X5) = ti(X1,X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,X4) != ti(X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_675]) ).

fof(i_0_1108,plain,
    ! [X3172,X3173] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3172),esk94_2(X3172,X3173)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3172)),X3173)) )
      & ( X3173 = hAPP(nat,nat,suc,esk94_2(X3172,X3173))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3172)),X3173)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_448_Suc__lessE])])])]) ).

fof(i_0_1109,plain,
    ! [X3021,X3022] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3021)),X3022))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3021),X3022)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_383_Suc__leD])]) ).

fof(i_0_1110,plain,
    ! [X3070,X3071] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3070),X3071))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3070)),X3071)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3070)),X3071))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3070),X3071)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_409_less__eq__Suc__le])]) ).

fof(i_0_1111,plain,
    ! [X3066,X3067] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3066)),X3067))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3066),X3067)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3066),X3067))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3066)),X3067)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_407_Suc__le__eq])]) ).

fof(i_0_1112,plain,
    ! [X3058,X3059] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3058)),X3059))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3058),X3059)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_403_Suc__le__lessD])]) ).

fof(i_0_1113,plain,
    ! [X3054,X3055] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3054)),X3055))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3054),X3055)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_400_Suc__lessD])]) ).

fof(i_0_1114,plain,
    ! [X3007,X3008] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3007),X3008))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3007)),hAPP(nat,nat,suc,X3008))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_375_Suc__mono])]) ).

cnf(i_0_1115,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3),hAPP(X1,X2,X3,X4)) = ti(X1,X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_676]) ).

cnf(i_0_1116,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1)
    | ti(X1,X3) != zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_677]) ).

cnf(i_0_1117,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_677]) ).

cnf(i_0_1118,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) != zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_677]) ).

fof(i_0_1119,plain,
    ! [X2070,X2071,X2072,X2073] :
      ( ~ preorder(X2070)
      | ~ hBOOL(hAPP(X2070,bool,hAPP(X2070,fun(X2070,bool),ord_less_eq(X2070),X2072),X2073))
      | ~ hBOOL(hAPP(X2070,bool,hAPP(X2070,fun(X2070,bool),ord_less_eq(X2070),X2073),X2071))
      | hBOOL(hAPP(X2070,bool,hAPP(X2070,fun(X2070,bool),ord_less_eq(X2070),X2072),X2071)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_97_order__trans])])]) ).

fof(i_0_1120,plain,
    ! [X2063,X2064,X2065,X2066] :
      ( ~ order(X2063)
      | ~ hBOOL(hAPP(X2063,bool,hAPP(X2063,fun(X2063,bool),ord_less_eq(X2063),X2065),X2066))
      | ~ hBOOL(hAPP(X2063,bool,hAPP(X2063,fun(X2063,bool),ord_less_eq(X2063),X2064),X2065))
      | hBOOL(hAPP(X2063,bool,hAPP(X2063,fun(X2063,bool),ord_less_eq(X2063),X2064),X2066)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_95_xt1_I6_J])])]) ).

fof(i_0_1121,plain,
    ! [X2169,X2170,X2171,X2172] :
      ( ~ preorder(X2169)
      | ~ hBOOL(hAPP(X2169,bool,hAPP(X2169,fun(X2169,bool),ord_less(X2169),X2171),X2172))
      | ~ hBOOL(hAPP(X2169,bool,hAPP(X2169,fun(X2169,bool),ord_less_eq(X2169),X2172),X2170))
      | hBOOL(hAPP(X2169,bool,hAPP(X2169,fun(X2169,bool),ord_less(X2169),X2171),X2170)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_126_order__less__le__trans])])]) ).

fof(i_0_1122,plain,
    ! [X2177,X2178,X2179,X2180] :
      ( ~ preorder(X2177)
      | ~ hBOOL(hAPP(X2177,bool,hAPP(X2177,fun(X2177,bool),ord_less_eq(X2177),X2179),X2180))
      | ~ hBOOL(hAPP(X2177,bool,hAPP(X2177,fun(X2177,bool),ord_less(X2177),X2180),X2178))
      | hBOOL(hAPP(X2177,bool,hAPP(X2177,fun(X2177,bool),ord_less(X2177),X2179),X2178)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_128_order__le__less__trans])])]) ).

fof(i_0_1123,plain,
    ! [X1926,X1927,X1928,X1929] :
      ( ~ preorder(X1926)
      | ~ hBOOL(hAPP(X1926,bool,hAPP(X1926,fun(X1926,bool),ord_less(X1926),X1928),X1929))
      | ~ hBOOL(hAPP(X1926,bool,hAPP(X1926,fun(X1926,bool),ord_less(X1926),X1929),X1927))
      | hBOOL(hAPP(X1926,bool,hAPP(X1926,fun(X1926,bool),ord_less(X1926),X1928),X1927)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_55_order__less__trans])])]) ).

fof(i_0_1124,plain,
    ! [X2173,X2174,X2175,X2176] :
      ( ~ order(X2173)
      | ~ hBOOL(hAPP(X2173,bool,hAPP(X2173,fun(X2173,bool),ord_less(X2173),X2175),X2176))
      | ~ hBOOL(hAPP(X2173,bool,hAPP(X2173,fun(X2173,bool),ord_less_eq(X2173),X2174),X2175))
      | hBOOL(hAPP(X2173,bool,hAPP(X2173,fun(X2173,bool),ord_less(X2173),X2174),X2176)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_127_xt1_I7_J])])]) ).

fof(i_0_1125,plain,
    ! [X2181,X2182,X2183,X2184] :
      ( ~ order(X2181)
      | ~ hBOOL(hAPP(X2181,bool,hAPP(X2181,fun(X2181,bool),ord_less_eq(X2181),X2183),X2184))
      | ~ hBOOL(hAPP(X2181,bool,hAPP(X2181,fun(X2181,bool),ord_less(X2181),X2182),X2183))
      | hBOOL(hAPP(X2181,bool,hAPP(X2181,fun(X2181,bool),ord_less(X2181),X2182),X2184)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_129_xt1_I8_J])])]) ).

fof(i_0_1126,plain,
    ! [X1922,X1923,X1924,X1925] :
      ( ~ order(X1922)
      | ~ hBOOL(hAPP(X1922,bool,hAPP(X1922,fun(X1922,bool),ord_less(X1922),X1924),X1925))
      | ~ hBOOL(hAPP(X1922,bool,hAPP(X1922,fun(X1922,bool),ord_less(X1922),X1923),X1924))
      | hBOOL(hAPP(X1922,bool,hAPP(X1922,fun(X1922,bool),ord_less(X1922),X1923),X1925)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_xt1_I10_J])])]) ).

fof(i_0_1127,plain,
    ! [X2624,X2625,X2626] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2625),X2626))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2626),X2624))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2625),X2624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_236_le__trans])]) ).

fof(i_0_1128,plain,
    ! [X2654,X2655,X2656,X2657] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2656),X2657))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2654),X2657) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2656),X2655)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2654),X2655)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_247_less__add__eq__less])]) ).

fof(i_0_1129,plain,
    ! [X3117,X3118,X3119,X3120] :
      ( ~ comm_semiring_1(X3117)
      | hAPP(X3117,X3117,hAPP(X3117,fun(X3117,X3117),plus_plus(X3117),hAPP(X3117,X3117,hAPP(X3117,fun(X3117,X3117),plus_plus(X3117),X3118),X3119)),X3120) = hAPP(X3117,X3117,hAPP(X3117,fun(X3117,X3117),plus_plus(X3117),X3118),hAPP(X3117,X3117,hAPP(X3117,fun(X3117,X3117),plus_plus(X3117),X3119),X3120)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])])]) ).

fof(i_0_1130,plain,
    ! [X2344,X2345,X2346,X2347] :
      ( ~ ab_semigroup_add(X2344)
      | hAPP(X2344,X2344,hAPP(X2344,fun(X2344,X2344),plus_plus(X2344),hAPP(X2344,X2344,hAPP(X2344,fun(X2344,X2344),plus_plus(X2344),X2345),X2346)),X2347) = hAPP(X2344,X2344,hAPP(X2344,fun(X2344,X2344),plus_plus(X2344),X2345),hAPP(X2344,X2344,hAPP(X2344,fun(X2344,X2344),plus_plus(X2344),X2346),X2347)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_166_ab__semigroup__add__class_Oadd__ac_I1_J])])]) ).

fof(i_0_1131,plain,
    ! [X3113,X3114,X3115,X3116] :
      ( ~ comm_semiring_1(X3113)
      | hAPP(X3113,X3113,hAPP(X3113,fun(X3113,X3113),plus_plus(X3113),X3114),hAPP(X3113,X3113,hAPP(X3113,fun(X3113,X3113),plus_plus(X3113),X3115),X3116)) = hAPP(X3113,X3113,hAPP(X3113,fun(X3113,X3113),plus_plus(X3113),hAPP(X3113,X3113,hAPP(X3113,fun(X3113,X3113),plus_plus(X3113),X3114),X3115)),X3116) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])])]) ).

fof(i_0_1132,plain,
    ! [X3060,X3061] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3061),hAPP(nat,nat,suc,X3060)))
        | X3061 = X3060
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3060),X3061)) )
      & ( X3061 != X3060
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3061),hAPP(nat,nat,suc,X3060)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3060),X3061)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_404_le__less__Suc__eq])])]) ).

fof(i_0_1133,plain,
    ! [X3035,X3036] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3035),X3036))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3036),hAPP(nat,nat,suc,X3035))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3036),hAPP(nat,nat,suc,X3035)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3035),X3036)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_678])]) ).

fof(i_0_1134,plain,
    ! [X2610,X2611,X2612] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2610),X2611)),X2612) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2610),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2611),X2612)),
    inference(variable_rename,[status(thm)],[fact_230_nat__add__assoc]) ).

fof(i_0_1135,plain,
    ! [X3047,X3048] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3047),X3048))
      | hAPP(nat,nat,suc,X3047) = X3048
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X3047)),X3048)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_397_Suc__lessI])]) ).

cnf(i_0_1136,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_679]) ).

cnf(i_0_1137,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_680]) ).

fof(i_0_1138,plain,
    ! [X3062,X3063] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3062),X3063))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3062)),X3063)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_405_Suc__leI])]) ).

fof(i_0_1139,plain,
    ! [X3105] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X3105))) = hAPP(nat,nat,suc,X3105),
    inference(variable_rename,[status(thm)],[fact_426_card__Collect__le__nat]) ).

fof(i_0_1140,plain,
    ! [X3201,X3202,X3203,X3204] :
      ( ~ hBOOL(hAPP(fun(X3202,bool),bool,finite_finite_1(X3202),X3204))
      | hBOOL(hAPP(fun(X3201,bool),bool,finite_finite_1(X3201),hAPP(fun(X3202,bool),fun(X3201,bool),hAPP(fun(X3202,X3201),fun(fun(X3202,bool),fun(X3201,bool)),image(X3202,X3201),X3203),X3204))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_459_finite__imageI])]) ).

cnf(i_0_1141,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_681]) ).

fof(i_0_1142,plain,
    ! [X3019,X3020] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3019),hAPP(nat,nat,suc,X3020)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3019),X3020))
      | X3019 = hAPP(nat,nat,suc,X3020) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_682])]) ).

fof(i_0_1143,plain,
    ! [X3013,X3014] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3013),hAPP(nat,nat,suc,X3014)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3013),X3014))
        | X3013 = hAPP(nat,nat,suc,X3014) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3013),X3014))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3013),hAPP(nat,nat,suc,X3014))) )
      & ( X3013 != hAPP(nat,nat,suc,X3014)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3013),hAPP(nat,nat,suc,X3014))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_379_le__Suc__eq])])]) ).

fof(i_0_1144,plain,
    ! [X3166,X3167] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3166)),X3167))
      | X3167 = hAPP(nat,nat,suc,esk92_2(X3166,X3167)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_446_Suc__le__D])])]) ).

fof(i_0_1145,plain,
    ! [X3140,X3141,X3142] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk86_3(X3140,X3141,X3142)),X3142))
        | hBOOL(hAPP(nat,bool,X3140,X3141))
        | ~ hBOOL(hAPP(nat,bool,X3140,X3142))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3141),X3142)) )
      & ( hBOOL(hAPP(nat,bool,X3140,hAPP(nat,nat,suc,esk86_3(X3140,X3141,X3142))))
        | hBOOL(hAPP(nat,bool,X3140,X3141))
        | ~ hBOOL(hAPP(nat,bool,X3140,X3142))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3141),X3142)) )
      & ( ~ hBOOL(hAPP(nat,bool,X3140,esk86_3(X3140,X3141,X3142)))
        | hBOOL(hAPP(nat,bool,X3140,X3141))
        | ~ hBOOL(hAPP(nat,bool,X3140,X3142))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3141),X3142)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_438_inc__induct])])])]) ).

fof(i_0_1146,plain,
    ! [X2130,X2131,X2132] :
      ( ( hBOOL(hAPP(X2130,bool,hAPP(X2130,fun(X2130,bool),ord_less_eq(X2130),X2131),X2132))
        | ~ hBOOL(hAPP(X2130,bool,hAPP(X2130,fun(X2130,bool),ord_less(X2130),X2131),X2132))
        | ~ preorder(X2130) )
      & ( ~ hBOOL(hAPP(X2130,bool,hAPP(X2130,fun(X2130,bool),ord_less_eq(X2130),X2132),X2131))
        | ~ hBOOL(hAPP(X2130,bool,hAPP(X2130,fun(X2130,bool),ord_less(X2130),X2131),X2132))
        | ~ preorder(X2130) )
      & ( ~ hBOOL(hAPP(X2130,bool,hAPP(X2130,fun(X2130,bool),ord_less_eq(X2130),X2131),X2132))
        | hBOOL(hAPP(X2130,bool,hAPP(X2130,fun(X2130,bool),ord_less_eq(X2130),X2132),X2131))
        | hBOOL(hAPP(X2130,bool,hAPP(X2130,fun(X2130,bool),ord_less(X2130),X2131),X2132))
        | ~ preorder(X2130) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_683])])])]) ).

fof(i_0_1147,plain,
    ! [X2792] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2792))) = X2792,
    inference(variable_rename,[status(thm)],[fact_290_card__Collect__less__nat]) ).

fof(i_0_1148,plain,
    ! [X3091,X3092,X3094,X3095,X3096] :
      ( ( X3091 = hAPP(nat,nat,suc,esk85_2(X3091,X3092))
        | X3091 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3091),hAPP(nat,nat,suc,X3092))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk85_2(X3091,X3092)),X3092))
        | X3091 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3091),hAPP(nat,nat,suc,X3092))) )
      & ( X3094 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3094),hAPP(nat,nat,suc,X3095))) )
      & ( X3094 != hAPP(nat,nat,suc,X3096)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3096),X3095))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3094),hAPP(nat,nat,suc,X3095))) ) ),
    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_417_less__Suc__eq__0__disj])])])])])]) ).

fof(i_0_1149,plain,
    ! [X2542,X2543,X2544] :
      ( ( hBOOL(hAPP(fun(X2542,bool),bool,hAPP(X2542,fun(fun(X2542,bool),bool),member(X2542),esk53_3(X2542,X2543,X2544)),X2544))
        | hBOOL(hAPP(fun(X2542,bool),bool,hAPP(fun(X2542,bool),fun(fun(X2542,bool),bool),ord_less_eq(fun(X2542,bool)),X2544),X2543)) )
      & ( ~ hBOOL(hAPP(fun(X2542,bool),bool,hAPP(X2542,fun(fun(X2542,bool),bool),member(X2542),esk53_3(X2542,X2543,X2544)),X2543))
        | hBOOL(hAPP(fun(X2542,bool),bool,hAPP(fun(X2542,bool),fun(fun(X2542,bool),bool),ord_less_eq(fun(X2542,bool)),X2544),X2543)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_211_subsetI])])])]) ).

fof(i_0_1150,plain,
    ! [X3224,X3225] :
      ( ~ hBOOL(hAPP(fun(X3224,bool),bool,finite_finite_1(X3224),top_top(fun(X3224,bool))))
      | ~ hBOOL(hAPP(fun(X3224,bool),bool,hAPP(fun(X3224,X3224),fun(fun(X3224,bool),bool),inj_on(X3224,X3224),X3225),top_top(fun(X3224,bool))))
      | hAPP(fun(X3224,bool),fun(X3224,bool),hAPP(fun(X3224,X3224),fun(fun(X3224,bool),fun(X3224,bool)),image(X3224,X3224),X3225),top_top(fun(X3224,bool))) = top_top(fun(X3224,bool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_466_finite__UNIV__inj__surj])]) ).

fof(i_0_1151,plain,
    ! [X3052,X3053] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3052),hAPP(nat,nat,suc,X3053)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3052),X3053))
      | X3052 = X3053 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_684])]) ).

fof(i_0_1152,plain,
    ! [X3043,X3044] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3043),X3044))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3043),hAPP(nat,nat,suc,X3044)))
      | X3044 = X3043 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_685])]) ).

fof(i_0_1153,plain,
    ! [X3041,X3042] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3041),hAPP(nat,nat,suc,X3042)))
        | X3041 = X3042
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3041),X3042)) )
      & ( X3041 != X3042
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3041),hAPP(nat,nat,suc,X3042)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3041),X3042)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_686])])]) ).

fof(i_0_1154,plain,
    ! [X3037,X3038] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3037),hAPP(nat,nat,suc,X3038)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3037),X3038))
        | X3037 = X3038 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3037),X3038))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3037),hAPP(nat,nat,suc,X3038))) )
      & ( X3037 != X3038
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3037),hAPP(nat,nat,suc,X3038))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_392_less__Suc__eq])])]) ).

fof(i_0_1155,plain,
    ! [X3068,X3069] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3068),hAPP(nat,nat,suc,X3069)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3068),X3069)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3068),X3069))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3068),hAPP(nat,nat,suc,X3069))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_408_less__Suc__eq__le])]) ).

cnf(i_0_1156,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_687]) ).

cnf(i_0_1157,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_688]) ).

cnf(i_0_1158,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_689]) ).

cnf(i_0_1159,plain,
    ( ti(X1,X3) = ti(X1,X2)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_690]) ).

fof(i_0_1160,plain,
    ! [X3010] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3010)),X3010)),
    inference(variable_rename,[status(thm)],[i_0_691]) ).

fof(i_0_1161,plain,
    ! [X2466,X2467,X2468] :
      ( ~ hBOOL(hAPP(fun(X2466,bool),bool,hAPP(fun(X2466,bool),fun(fun(X2466,bool),bool),ord_less(fun(X2466,bool)),X2467),X2468))
      | hBOOL(hAPP(fun(X2466,bool),bool,hAPP(fun(X2466,bool),fun(fun(X2466,bool),bool),ord_less_eq(fun(X2466,bool)),X2467),X2468)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_192_psubset__imp__subset])]) ).

fof(i_0_1162,plain,
    ! [X2864,X2866,X2867,X2868] :
      ( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2864))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2866),X2864))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2866),esk73_1(X2864))) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk74_2(X2867,X2868)),X2867))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2867)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk74_2(X2867,X2868)),X2868))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2867)) ) ),
    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_313_finite__nat__set__iff__bounded__le])])])])])]) ).

fof(i_0_1163,plain,
    ! [X2870,X2872,X2873,X2874] :
      ( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2870))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2872),X2870))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2872),esk75_1(X2870))) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk76_2(X2873,X2874)),X2873))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2873)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk76_2(X2873,X2874)),X2874))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2873)) ) ),
    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_314_finite__nat__set__iff__bounded])])])])])]) ).

fof(i_0_1164,plain,
    ! [X2983,X2984,X2986] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk79_2(X2983,X2984)),X2983))
        | ~ hBOOL(hAPP(nat,bool,X2984,X2983))
        | hBOOL(hAPP(nat,bool,X2984,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2986),esk79_2(X2983,X2984)))
        | ~ hBOOL(hAPP(nat,bool,X2984,X2986))
        | ~ hBOOL(hAPP(nat,bool,X2984,X2983))
        | hBOOL(hAPP(nat,bool,X2984,zero_zero(nat))) )
      & ( hBOOL(hAPP(nat,bool,X2984,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk79_2(X2983,X2984)),one_one(nat))))
        | ~ hBOOL(hAPP(nat,bool,X2984,X2983))
        | hBOOL(hAPP(nat,bool,X2984,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_692])])])])]) ).

fof(i_0_1165,plain,
    ! [X3226,X3227] :
      ( ~ hBOOL(hAPP(fun(X3226,bool),bool,finite_finite_1(X3226),top_top(fun(X3226,bool))))
      | hAPP(fun(X3226,bool),fun(X3226,bool),hAPP(fun(X3226,X3226),fun(fun(X3226,bool),fun(X3226,bool)),image(X3226,X3226),X3227),top_top(fun(X3226,bool))) != top_top(fun(X3226,bool))
      | hBOOL(hAPP(fun(X3226,bool),bool,hAPP(fun(X3226,X3226),fun(fun(X3226,bool),bool),inj_on(X3226,X3226),X3227),top_top(fun(X3226,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_467_finite__UNIV__surj__inj])]) ).

fof(i_0_1166,plain,
    ! [X1952,X1953,X1954,X1955] :
      ( ~ preorder(X1952)
      | ~ hBOOL(hAPP(X1952,bool,hAPP(X1952,fun(X1952,bool),ord_less(X1952),X1954),X1955))
      | ~ hBOOL(hAPP(X1952,bool,hAPP(X1952,fun(X1952,bool),ord_less(X1952),X1955),X1954))
      | hBOOL(X1953) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_62_order__less__imp__triv])])]) ).

fof(i_0_1167,plain,
    ! [X1946,X1947,X1948] :
      ( ~ order(X1946)
      | ~ hBOOL(hAPP(X1946,bool,hAPP(X1946,fun(X1946,bool),ord_less(X1946),X1947),X1948))
      | ~ hBOOL(hAPP(X1946,bool,hAPP(X1946,fun(X1946,bool),ord_less(X1946),X1948),X1947)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_693])])]) ).

fof(i_0_1168,plain,
    ! [X1965,X1966,X1967] :
      ( ~ preorder(X1965)
      | ~ hBOOL(hAPP(X1965,bool,hAPP(X1965,fun(X1965,bool),ord_less(X1965),X1966),X1967))
      | ~ hBOOL(hAPP(X1965,bool,hAPP(X1965,fun(X1965,bool),ord_less(X1965),X1967),X1966)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_694])])]) ).

fof(i_0_1169,plain,
    ! [X1962,X1963,X1964] :
      ( ~ preorder(X1962)
      | ~ hBOOL(hAPP(X1962,bool,hAPP(X1962,fun(X1962,bool),ord_less(X1962),X1963),X1964))
      | ~ hBOOL(hAPP(X1962,bool,hAPP(X1962,fun(X1962,bool),ord_less(X1962),X1964),X1963)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_695])])]) ).

fof(i_0_1170,plain,
    ! [X1949,X1950,X1951] :
      ( ~ preorder(X1949)
      | ~ hBOOL(hAPP(X1949,bool,hAPP(X1949,fun(X1949,bool),ord_less(X1949),X1950),X1951))
      | ~ hBOOL(hAPP(X1949,bool,hAPP(X1949,fun(X1949,bool),ord_less(X1949),X1951),X1950)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_696])])]) ).

fof(i_0_1171,plain,
    ! [X1919,X1920,X1921] :
      ( ~ preorder(X1919)
      | ~ hBOOL(hAPP(X1919,bool,hAPP(X1919,fun(X1919,bool),ord_less(X1919),X1920),X1921))
      | ~ hBOOL(hAPP(X1919,bool,hAPP(X1919,fun(X1919,bool),ord_less(X1919),X1921),X1920)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_697])])]) ).

fof(i_0_1172,plain,
    ! [X2121,X2122,X2123] :
      ( ( hBOOL(hAPP(X2121,bool,hAPP(X2121,fun(X2121,bool),ord_less_eq(X2121),X2122),X2123))
        | hBOOL(hAPP(X2121,bool,hAPP(X2121,fun(X2121,bool),ord_less(X2121),X2123),X2122))
        | ~ linorder(X2121) )
      & ( ~ hBOOL(hAPP(X2121,bool,hAPP(X2121,fun(X2121,bool),ord_less(X2121),X2123),X2122))
        | ~ hBOOL(hAPP(X2121,bool,hAPP(X2121,fun(X2121,bool),ord_less_eq(X2121),X2122),X2123))
        | ~ linorder(X2121) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_698])])])]) ).

fof(i_0_1173,plain,
    ! [X2151,X2152,X2153] :
      ( ~ linorder(X2151)
      | ~ hBOOL(hAPP(X2151,bool,hAPP(X2151,fun(X2151,bool),ord_less_eq(X2151),X2152),X2153))
      | ~ hBOOL(hAPP(X2151,bool,hAPP(X2151,fun(X2151,bool),ord_less(X2151),X2153),X2152)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_699])])]) ).

fof(i_0_1174,plain,
    ! [X2118,X2119,X2120] :
      ( ( hBOOL(hAPP(X2118,bool,hAPP(X2118,fun(X2118,bool),ord_less(X2118),X2119),X2120))
        | hBOOL(hAPP(X2118,bool,hAPP(X2118,fun(X2118,bool),ord_less_eq(X2118),X2120),X2119))
        | ~ linorder(X2118) )
      & ( ~ hBOOL(hAPP(X2118,bool,hAPP(X2118,fun(X2118,bool),ord_less_eq(X2118),X2120),X2119))
        | ~ hBOOL(hAPP(X2118,bool,hAPP(X2118,fun(X2118,bool),ord_less(X2118),X2119),X2120))
        | ~ linorder(X2118) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_700])])])]) ).

fof(i_0_1175,plain,
    ! [X3017,X3018] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3017),X3018))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3017),hAPP(nat,nat,suc,X3018))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_381_le__SucI])]) ).

fof(i_0_1176,plain,
    ! [X3064,X3065] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3064),X3065))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3064),hAPP(nat,nat,suc,X3065))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_406_le__imp__less__Suc])]) ).

fof(i_0_1177,plain,
    ! [X3045,X3046] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3045),X3046))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3045),hAPP(nat,nat,suc,X3046))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_396_less__SucI])]) ).

fof(i_0_1178,plain,
    ! [X2979] :
      ( ~ linordered_semidom(X2979)
      | hBOOL(hAPP(X2979,bool,hAPP(X2979,fun(X2979,bool),ord_less(X2979),zero_zero(X2979)),hAPP(X2979,X2979,hAPP(X2979,fun(X2979,X2979),plus_plus(X2979),one_one(X2979)),one_one(X2979)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_363_zero__less__two])]) ).

fof(i_0_1179,plain,
    ! [X2627,X2628] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2627),X2628))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2628),X2627))
      | X2627 = X2628 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_237_le__antisym])]) ).

cnf(i_0_1180,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_688]) ).

cnf(i_0_1181,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_701]) ).

cnf(i_0_1182,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_702]) ).

cnf(i_0_1183,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_703]) ).

cnf(i_0_1184,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_704]) ).

cnf(i_0_1185,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_705]) ).

fof(i_0_1186,plain,
    ! [X2275,X2276] :
      ( ~ linordered_semidom(X2275)
      | hBOOL(hAPP(X2275,bool,hAPP(X2275,fun(X2275,bool),ord_less(X2275),X2276),hAPP(X2275,X2275,hAPP(X2275,fun(X2275,X2275),plus_plus(X2275),X2276),one_one(X2275)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_less__add__one])])]) ).

fof(i_0_1187,plain,
    ! [X3109,X3110,X3111,X3112] :
      ( ~ comm_semiring_1(X3109)
      | hAPP(X3109,X3109,hAPP(X3109,fun(X3109,X3109),plus_plus(X3109),X3110),hAPP(X3109,X3109,hAPP(X3109,fun(X3109,X3109),plus_plus(X3109),X3111),X3112)) = hAPP(X3109,X3109,hAPP(X3109,fun(X3109,X3109),plus_plus(X3109),X3111),hAPP(X3109,X3109,hAPP(X3109,fun(X3109,X3109),plus_plus(X3109),X3110),X3112)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])])]) ).

fof(i_0_1188,plain,
    ! [X2292,X2293,X2294] :
      ( ( hBOOL(hAPP(X2292,bool,hAPP(X2292,fun(X2292,bool),ord_less(X2292),esk37_3(X2292,X2293,X2294)),X2294))
        | hBOOL(hAPP(X2292,bool,hAPP(X2292,fun(X2292,bool),ord_less_eq(X2292),X2294),X2293))
        | ~ dense_linorder(X2292) )
      & ( ~ hBOOL(hAPP(X2292,bool,hAPP(X2292,fun(X2292,bool),ord_less_eq(X2292),esk37_3(X2292,X2293,X2294)),X2293))
        | hBOOL(hAPP(X2292,bool,hAPP(X2292,fun(X2292,bool),ord_less_eq(X2292),X2294),X2293))
        | ~ dense_linorder(X2292) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_153_dense__le])])])])]) ).

fof(i_0_1189,plain,
    ! [X2980,X2981] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X2980,bool),nat,finite_card(X2980),X2981)))
      | hBOOL(hAPP(fun(X2980,bool),bool,finite_finite_1(X2980),X2981)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_364_card__ge__0__finite])]) ).

fof(i_0_1190,plain,
    ! [X2793,X2794,X2795] :
      ( ~ hBOOL(hAPP(fun(X2793,bool),bool,hAPP(fun(X2793,bool),fun(fun(X2793,bool),bool),ord_less_eq(fun(X2793,bool)),X2794),X2795))
      | ~ hBOOL(hAPP(fun(X2793,bool),bool,finite_finite_1(X2793),X2795))
      | hBOOL(hAPP(fun(X2793,bool),bool,finite_finite_1(X2793),X2794)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_291_finite__subset])]) ).

fof(i_0_1191,plain,
    ! [X2796,X2797,X2798] :
      ( ~ hBOOL(hAPP(fun(X2796,bool),bool,finite_finite_1(X2796),X2798))
      | ~ hBOOL(hAPP(fun(X2796,bool),bool,hAPP(fun(X2796,bool),fun(fun(X2796,bool),bool),ord_less_eq(fun(X2796,bool)),X2797),X2798))
      | hBOOL(hAPP(fun(X2796,bool),bool,finite_finite_1(X2796),X2797)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_292_rev__finite__subset])]) ).

fof(i_0_1192,plain,
    ! [X2673,X2674] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2673),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2673),X2674))),
    inference(variable_rename,[status(thm)],[fact_255_le__add1]) ).

fof(i_0_1193,plain,
    ! [X2671,X2672] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2671),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2672),X2671))),
    inference(variable_rename,[status(thm)],[fact_254_le__add2]) ).

fof(i_0_1194,plain,
    ! [X2602,X2603,X2604] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | X2603 = X2604
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2603),X2604)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | X2603 = X2604
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2603),X2604)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2603),X2604)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2603),X2604)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | X2603 = X2604
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | X2603 = X2604
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2602,X2604),X2603)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_227_nat__less__cases])])]) ).

fof(i_0_1195,plain,
    ! [X2607,X2608,X2609] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2607),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2608),X2609)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2608),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2607),X2609)),
    inference(variable_rename,[status(thm)],[fact_229_nat__add__left__commute]) ).

cnf(i_0_1196,plain,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_706]) ).

cnf(i_0_1197,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_707]) ).

cnf(i_0_1198,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_708]) ).

cnf(i_0_1199,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_709]) ).

cnf(i_0_1200,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_710]) ).

cnf(i_0_1201,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_711]) ).

cnf(i_0_1202,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_681]) ).

cnf(i_0_1203,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_712]) ).

cnf(i_0_1204,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_713]) ).

cnf(i_0_1205,plain,
    ( hAPP(X1,X4,X5,X2) = hAPP(X1,X4,X5,X3)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_714]) ).

cnf(i_0_1206,plain,
    ( ti(X1,X4) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_715]) ).

cnf(i_0_1207,plain,
    ( ti(X1,X4) = ti(X1,X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_714]) ).

fof(i_0_1208,plain,
    ! [X2990,X2991,X2993] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk81_2(X2990,X2991)),X2990))
        | ~ hBOOL(hAPP(nat,bool,X2991,X2990))
        | hBOOL(hAPP(nat,bool,X2991,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2993),esk81_2(X2990,X2991)))
        | ~ hBOOL(hAPP(nat,bool,X2991,X2993))
        | ~ hBOOL(hAPP(nat,bool,X2991,X2990))
        | hBOOL(hAPP(nat,bool,X2991,zero_zero(nat))) )
      & ( hBOOL(hAPP(nat,bool,X2991,esk81_2(X2990,X2991)))
        | ~ hBOOL(hAPP(nat,bool,X2991,X2990))
        | hBOOL(hAPP(nat,bool,X2991,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_716])])])])]) ).

fof(i_0_1209,plain,
    ! [X2504,X2505,X2506,X2507] :
      ( ~ hBOOL(hAPP(fun(X2504,bool),bool,hAPP(fun(X2504,bool),fun(fun(X2504,bool),bool),ord_less_eq(fun(X2504,bool)),X2506),X2507))
      | ~ hBOOL(hAPP(X2504,bool,X2506,X2505))
      | hBOOL(hAPP(X2504,bool,X2507,X2505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_201_predicate1D])]) ).

fof(i_0_1210,plain,
    ! [X2518,X2519,X2520,X2521] :
      ( ~ hBOOL(hAPP(X2518,bool,X2520,X2521))
      | ~ hBOOL(hAPP(fun(X2518,bool),bool,hAPP(fun(X2518,bool),fun(fun(X2518,bool),bool),ord_less_eq(fun(X2518,bool)),X2520),X2519))
      | hBOOL(hAPP(X2518,bool,X2519,X2521)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_205_rev__predicate1D])]) ).

fof(i_0_1211,plain,
    ! [X2814,X2815] :
      ( hBOOL(hAPP(fun(X2814,bool),bool,finite_finite_1(X2814),top_top(fun(X2814,bool))))
      | ~ hBOOL(hAPP(fun(X2814,bool),bool,finite_finite_1(X2814),X2815))
      | ~ hBOOL(hAPP(fun(X2814,bool),bool,hAPP(X2814,fun(fun(X2814,bool),bool),member(X2814),esk72_2(X2814,X2815)),X2815)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_717])])])])]) ).

cnf(i_0_1212,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_char_0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_718]) ).

cnf(i_0_1213,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk26_2(X1,X2)),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_654]) ).

fof(i_0_1214,plain,
    ! [X3072,X3073,X3075,X3076,X3077] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3072),X3073))
        | X3073 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3072),esk83_2(X3072,X3073))) )
      & ( X3076 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3075),X3077))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3075),X3076)) ) ),
    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_410_less__iff__Suc__add])])])])]) ).

cnf(i_0_1215,plain,
    ( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_680]) ).

fof(i_0_1216,plain,
    ! [X3409,X3410,X3411,X3412,X3413,X3414] : hAPP(X3409,X3410,hAPP(fun(X3409,X3411),fun(X3409,X3410),hAPP(fun(X3409,fun(X3411,X3410)),fun(fun(X3409,X3411),fun(X3409,X3410)),combs(X3409,X3411,X3410),X3412),X3413),X3414) = hAPP(X3411,X3410,hAPP(X3409,fun(X3411,X3410),X3412,X3414),hAPP(X3409,X3411,X3413,X3414)),
    inference(variable_rename,[status(thm)],[help_COMBS_1_1_U]) ).

cnf(i_0_1217,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,esk69_4(X2,X1,X3,X4)) != ti(X1,esk70_4(X2,X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_719]) ).

cnf(i_0_1218,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,esk30_4(X1,X2,X3,X4)) != ti(X1,esk31_4(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_658]) ).

fof(i_0_1219,plain,
    ! [X3169,X3170] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3169),esk93_2(X3169,X3170)))
        | X3170 = hAPP(nat,nat,suc,X3169)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3169),X3170)) )
      & ( X3170 = hAPP(nat,nat,suc,esk93_2(X3169,X3170))
        | X3170 = hAPP(nat,nat,suc,X3169)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3169),X3170)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_lessE])])])]) ).

fof(i_0_1220,plain,
    ! [X3144,X3145] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3144),X3145))
      | X3145 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3144),esk87_2(X3144,X3145))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_439_less__imp__Suc__add])])]) ).

fof(i_0_1221,plain,
    ! [X2154,X2155,X2156] :
      ( ~ preorder(X2154)
      | ~ hBOOL(hAPP(X2154,bool,hAPP(X2154,fun(X2154,bool),ord_less(X2154),X2155),X2156))
      | hBOOL(hAPP(X2154,bool,hAPP(X2154,fun(X2154,bool),ord_less_eq(X2154),X2155),X2156)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_121_order__less__imp__le])])]) ).

cnf(i_0_1222,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_char_0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_718]) ).

cnf(i_0_1223,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Odictator_res]) ).

fof(i_0_1224,plain,
    ! [X3205,X3206] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3205),X3206))),
    inference(variable_rename,[status(thm)],[fact_460_finite__atLeastLessThan]) ).

fof(i_0_1225,plain,
    ! [X2994,X2995] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk82_2(X2994,X2995)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2994),X2995)) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2994),esk82_2(X2994,X2995)) = X2995
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2994),X2995)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_369_less__imp__add__positive])])])]) ).

cnf(i_0_1226,plain,
    ti(fun(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)))),finite_fold_image(nat,X1)) = finite_fold_image(nat,X1),
    inference(split_conjunct,[status(thm)],[i_0_720]) ).

fof(i_0_1227,plain,
    ! [X1884,X1885,X1886,X1887,X1888,X1889] : hAPP(product_prod(X1884,X1885),X1886,hAPP(fun(X1884,fun(X1885,X1886)),fun(product_prod(X1884,X1885),X1886),product_prod_rec(X1884,X1885,X1886),X1887),hAPP(X1885,product_prod(X1884,X1885),hAPP(X1884,fun(X1885,product_prod(X1884,X1885)),product_Pair(X1884,X1885),X1888),X1889)) = hAPP(X1885,X1886,hAPP(X1884,fun(X1885,X1886),X1887,X1888),X1889),
    inference(variable_rename,[status(thm)],[fact_28_prod_Orecs]) ).

fof(i_0_1228,plain,
    ! [X2667,X2668] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2667),X2668))
      | X2667 = X2668
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2667),X2668)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_252_le__neq__implies__less])]) ).

fof(i_0_1229,plain,
    ! [X2663,X2664] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2663),X2664))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2663),X2664))
        | X2663 = X2664 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2663),X2664))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2663),X2664)) )
      & ( X2663 != X2664
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2663),X2664)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_250_le__eq__less__or__eq])])]) ).

fof(i_0_1230,plain,
    ! [X2661,X2662] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2661),X2662))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2661),X2662)) )
      & ( X2661 != X2662
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2661),X2662)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2661),X2662))
        | X2661 = X2662
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2661),X2662)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_249_nat__less__le])])]) ).

fof(i_0_1231,plain,
    ! [X2719,X2720] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2719),X2720))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2719),X2720)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_268_termination__basic__simps_I5_J])]) ).

fof(i_0_1232,plain,
    ! [X2669,X2670] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2669),X2670))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2669),X2670)) )
      & ( X2669 != X2670
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2669),X2670)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_253_less__or__eq__imp__le])])]) ).

fof(i_0_1233,plain,
    ! [X2665,X2666] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2665),X2666))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2665),X2666)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_251_less__imp__le__nat])]) ).

fof(i_0_1234,plain,
    ! [X3090] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3090),hAPP(nat,nat,suc,zero_zero(nat))))
        | X3090 = zero_zero(nat) )
      & ( X3090 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3090),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_416_less__Suc0])]) ).

cnf(i_0_1235,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_712]) ).

cnf(i_0_1236,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Ounanimity_res]) ).

cnf(i_0_1237,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OIIA_res]) ).

fof(i_0_1238,plain,
    ! [X2982] :
      ( ~ hBOOL(hAPP(fun(X2982,bool),bool,finite_finite_1(X2982),top_top(fun(X2982,bool))))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X2982,bool),nat,finite_card(X2982),top_top(fun(X2982,bool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_365_finite__UNIV__card__ge__0])]) ).

fof(i_0_1239,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk66_0),arrow_2064824852le_Lin)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_271_linear__alt])]) ).

fof(i_0_1240,plain,
    ! [X3182,X3183] :
      ( ( hBOOL(hAPP(nat,bool,X3183,esk98_2(X3182,X3183)))
        | hBOOL(hAPP(nat,bool,X3183,X3182))
        | ~ hBOOL(hAPP(nat,bool,X3183,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,X3183,hAPP(nat,nat,suc,esk98_2(X3182,X3183))))
        | hBOOL(hAPP(nat,bool,X3183,X3182))
        | ~ hBOOL(hAPP(nat,bool,X3183,zero_zero(nat))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_452_nat__induct])])])]) ).

cnf(i_0_1241,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linordered_idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_721]) ).

cnf(i_0_1242,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_722]) ).

cnf(i_0_1243,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X2) = ti(X1,X3)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_723]) ).

cnf(i_0_1244,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_724]) ).

cnf(i_0_1245,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_703]) ).

cnf(i_0_1246,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_725]) ).

cnf(i_0_1247,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_726]) ).

fof(i_0_1248,plain,
    ! [X3391,X3392,X3393,X3394,X3395,X3396] : hAPP(X3391,X3392,hAPP(fun(X3391,X3393),fun(X3391,X3392),hAPP(fun(X3393,X3392),fun(fun(X3391,X3393),fun(X3391,X3392)),combb(X3393,X3392,X3391),X3394),X3395),X3396) = hAPP(X3393,X3392,X3394,hAPP(X3391,X3393,X3395,X3396)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_U]) ).

fof(i_0_1249,plain,
    ! [X3397,X3398,X3399,X3400,X3401,X3402] : hAPP(X3397,X3398,hAPP(X3399,fun(X3397,X3398),hAPP(fun(X3397,fun(X3399,X3398)),fun(X3399,fun(X3397,X3398)),combc(X3397,X3399,X3398),X3400),X3401),X3402) = hAPP(X3399,X3398,hAPP(X3397,fun(X3399,X3398),X3400,X3402),X3401),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_U]) ).

cnf(i_0_1250,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,product_prod(X4,X1),hAPP(X4,fun(X1,product_prod(X4,X1)),product_Pair(X4,X1),X5),X2) != hAPP(X1,product_prod(X4,X1),hAPP(X4,fun(X1,product_prod(X4,X1)),product_Pair(X4,X1),X6),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_727]) ).

cnf(i_0_1251,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,product_prod(X4,X1),hAPP(X4,fun(X1,product_prod(X4,X1)),product_Pair(X4,X1),X5),X2) != hAPP(X1,product_prod(X4,X1),hAPP(X4,fun(X1,product_prod(X4,X1)),product_Pair(X4,X1),X6),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_728]) ).

cnf(i_0_1252,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X2),X5) != hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X3),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_727]) ).

cnf(i_0_1253,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X2),X5) != hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X3),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_728]) ).

fof(i_0_1254,plain,
    ! [X3031,X3032] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X3031)),X3032) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3031),X3032)),
    inference(variable_rename,[status(thm)],[fact_389_add__Suc]) ).

cnf(i_0_1255,plain,
    ( hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X2),X5) = hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X3),X6)
    | ti(X1,X2) != ti(X1,X3)
    | ti(X4,X5) != ti(X4,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_727]) ).

cnf(i_0_1256,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Obelow_res]) ).

cnf(i_0_1257,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Oabove_res]) ).

fof(i_0_1258,plain,
    ! [X1994,X1995,X1996] :
      ( ( ~ hBOOL(hAPP(fun(X1994,bool),bool,hAPP(X1994,fun(fun(X1994,bool),bool),member(X1994),X1995),X1996))
        | hBOOL(hAPP(X1994,bool,X1996,X1995)) )
      & ( ~ hBOOL(hAPP(X1994,bool,X1996,X1995))
        | hBOOL(hAPP(fun(X1994,bool),bool,hAPP(X1994,fun(fun(X1994,bool),bool),member(X1994),X1995),X1996)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_76_mem__def])]) ).

cnf(i_0_1259,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_711]) ).

cnf(i_0_1260,plain,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_729]) ).

cnf(i_0_1261,plain,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_730]) ).

cnf(i_0_1262,plain,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_731]) ).

cnf(i_0_1263,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_722]) ).

cnf(i_0_1264,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X2)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_722]) ).

cnf(i_0_1265,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_723]) ).

fof(i_0_1266,plain,
    ! [X2675,X2676,X2678,X2679,X2680] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2675),X2676))
        | X2676 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2675),esk60_2(X2675,X2676)) )
      & ( X2679 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2678),X2680)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2678),X2679)) ) ),
    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_256_le__iff__add])])])])]) ).

cnf(i_0_1267,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,esk35_3(X1,X2,X3)) != ti(X1,esk36_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_732]) ).

fof(i_0_1268,plain,
    ! [X2107,X2108,X2109] :
      ( ~ linorder(X2107)
      | hBOOL(hAPP(X2107,bool,hAPP(X2107,fun(X2107,bool),ord_less_eq(X2107),X2108),X2109))
      | hBOOL(hAPP(X2107,bool,hAPP(X2107,fun(X2107,bool),ord_less_eq(X2107),X2109),X2108)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_107_linorder__linear])])]) ).

fof(i_0_1269,plain,
    ! [X2055,X2056,X2057] :
      ( ~ linorder(X2055)
      | hBOOL(hAPP(X2055,bool,hAPP(X2055,fun(X2055,bool),ord_less_eq(X2055),X2056),X2057))
      | hBOOL(hAPP(X2055,bool,hAPP(X2055,fun(X2055,bool),ord_less_eq(X2055),X2057),X2056)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_733])])]) ).

fof(i_0_1270,plain,
    ! [X2136,X2137,X2138] :
      ( ~ linorder(X2136)
      | hBOOL(hAPP(X2136,bool,hAPP(X2136,fun(X2136,bool),ord_less(X2136),X2137),X2138))
      | hBOOL(hAPP(X2136,bool,hAPP(X2136,fun(X2136,bool),ord_less_eq(X2136),X2138),X2137)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_734])])]) ).

fof(i_0_1271,plain,
    ! [X2139,X2140,X2141] :
      ( ~ linorder(X2139)
      | hBOOL(hAPP(X2139,bool,hAPP(X2139,fun(X2139,bool),ord_less_eq(X2139),X2140),X2141))
      | hBOOL(hAPP(X2139,bool,hAPP(X2139,fun(X2139,bool),ord_less(X2139),X2141),X2140)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_735])])]) ).

fof(i_0_1272,plain,
    ! [X2124,X2125,X2126] :
      ( ~ linorder(X2124)
      | hBOOL(hAPP(X2124,bool,hAPP(X2124,fun(X2124,bool),ord_less_eq(X2124),X2125),X2126))
      | hBOOL(hAPP(X2124,bool,hAPP(X2124,fun(X2124,bool),ord_less(X2124),X2126),X2125)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_111_linorder__le__less__linear])])]) ).

cnf(i_0_1273,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_673]) ).

cnf(i_0_1274,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_673]) ).

cnf(i_0_1275,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_736]) ).

cnf(i_0_1276,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_737]) ).

cnf(i_0_1277,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_737]) ).

cnf(i_0_1278,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_679]) ).

cnf(i_0_1279,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_738]) ).

fof(i_0_1280,plain,
    ! [X2879,X2880] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk78_2(X2879,X2880)),X2880))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2880)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk78_2(X2879,X2880)),X2879))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2880)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_316_bounded__nat__set__is__finite])])])]) ).

fof(i_0_1281,plain,
    ! [X2802,X2803] :
      ( ( hBOOL(hAPP(fun(X2802,bool),bool,finite_finite_1(X2802),top_top(fun(X2802,bool))))
        | ~ hBOOL(hAPP(fun(sum_sum(X2802,X2803),bool),bool,finite_finite_1(sum_sum(X2802,X2803)),top_top(fun(sum_sum(X2802,X2803),bool)))) )
      & ( hBOOL(hAPP(fun(X2803,bool),bool,finite_finite_1(X2803),top_top(fun(X2803,bool))))
        | ~ hBOOL(hAPP(fun(sum_sum(X2802,X2803),bool),bool,finite_finite_1(sum_sum(X2802,X2803)),top_top(fun(sum_sum(X2802,X2803),bool)))) )
      & ( ~ hBOOL(hAPP(fun(X2802,bool),bool,finite_finite_1(X2802),top_top(fun(X2802,bool))))
        | ~ hBOOL(hAPP(fun(X2803,bool),bool,finite_finite_1(X2803),top_top(fun(X2803,bool))))
        | hBOOL(hAPP(fun(sum_sum(X2802,X2803),bool),bool,finite_finite_1(sum_sum(X2802,X2803)),top_top(fun(sum_sum(X2802,X2803),bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_295_finite__Plus__UNIV__iff])])]) ).

fof(i_0_1282,plain,
    ! [X2800,X2801] :
      ( ~ hBOOL(hAPP(fun(X2801,bool),bool,finite_finite_1(X2801),top_top(fun(X2801,bool))))
      | ~ hBOOL(hAPP(fun(X2800,bool),bool,finite_finite_1(X2800),top_top(fun(X2800,bool))))
      | hBOOL(hAPP(fun(product_prod(X2801,X2800),bool),bool,finite_finite_1(product_prod(X2801,X2800)),top_top(fun(product_prod(X2801,X2800),bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_294_finite__Prod__UNIV])]) ).

cnf(i_0_1283,plain,
    ti(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),pi(X1,X2)) = pi(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_739]) ).

fof(i_0_1284,plain,
    ! [X2595,X2596] :
      ( X2595 = X2596
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2595),X2596))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2596),X2595)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_740])]) ).

fof(i_0_1285,plain,
    ! [X2593,X2594] :
      ( ( X2593 = X2594
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2593),X2594))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2594),X2593)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2593),X2594))
        | X2593 != X2594 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2594),X2593))
        | X2593 != X2594 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_222_nat__neq__iff])])]) ).

fof(i_0_1286,plain,
    ! [X2620,X2621] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2620),X2621))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2621),X2620)) ),
    inference(variable_rename,[status(thm)],[fact_234_nat__le__linear]) ).

fof(i_0_1287,plain,
    ! [X2987,X2988] :
      ( ( hBOOL(hAPP(fun(X2987,bool),bool,hAPP(X2987,fun(fun(X2987,bool),bool),member(X2987),esk80_2(X2987,X2988)),X2988))
        | hAPP(fun(X2987,bool),nat,finite_card(X2987),X2988) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X2987,bool),bool,finite_finite_1(X2987),X2988)) )
      & ( one_one(nat) != zero_zero(nat)
        | hAPP(fun(X2987,bool),nat,finite_card(X2987),X2988) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X2987,bool),bool,finite_finite_1(X2987),X2988)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_367_card_Oneutral])])])]) ).

fof(i_0_1288,plain,
    ! [X3033,X3034] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3033),hAPP(nat,nat,suc,X3034)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3033),X3034)),
    inference(variable_rename,[status(thm)],[fact_390_add__Suc__right]) ).

cnf(i_0_1289,plain,
    ( ti(X1,X2) = ti(X1,X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_741]) ).

cnf(i_0_1290,plain,
    ( ti(X1,X2) = ti(X1,X4)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_742]) ).

cnf(i_0_1291,plain,
    ( ti(X1,X3) = ti(X1,X4)
    | ~ cancel146912293up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_743]) ).

cnf(i_0_1292,plain,
    ( ti(X1,X3) = ti(X1,X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_744]) ).

cnf(i_0_1293,plain,
    ( ti(X1,X3) = ti(X1,X4)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_745]) ).

cnf(i_0_1294,plain,
    ( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
    | hAPP(X1,X2,X3,esk20_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk20_4(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_746]) ).

cnf(i_0_1295,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_747]) ).

fof(i_0_1296,plain,
    ! [X3029,X3030] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X3029)),X3030) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3029),hAPP(nat,nat,suc,X3030)),
    inference(variable_rename,[status(thm)],[fact_388_add__Suc__shift]) ).

cnf(i_0_1297,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1)))
    | ti(X1,X2) != top_top(X1)
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_748]) ).

fof(i_0_1298,plain,
    ! [X3001,X3002] :
      ( ~ hBOOL(hAPP(fun(fun(X3001,X3002),bool),bool,finite_finite_1(fun(X3001,X3002)),top_top(fun(fun(X3001,X3002),bool))))
      | hAPP(fun(X3002,bool),nat,finite_card(X3002),top_top(fun(X3002,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
      | hBOOL(hAPP(fun(X3001,bool),bool,finite_finite_1(X3001),top_top(fun(X3001,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_372_finite__fun__UNIVD1])]) ).

cnf(i_0_1299,plain,
    ( ti(X1,X2) = top_top(X1)
    | ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_749]) ).

cnf(i_0_1300,plain,
    ( ti(X1,X2) = top_top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_750]) ).

fof(i_0_1301,plain,
    ! [X3179,X3180] :
      ( ( hBOOL(hAPP(nat,bool,X3179,hAPP(nat,nat,suc,esk97_1(X3179))))
        | hBOOL(hAPP(nat,bool,X3179,zero_zero(nat)))
        | ~ hBOOL(hAPP(nat,bool,X3179,X3180)) )
      & ( ~ hBOOL(hAPP(nat,bool,X3179,esk97_1(X3179)))
        | hBOOL(hAPP(nat,bool,X3179,zero_zero(nat)))
        | ~ hBOOL(hAPP(nat,bool,X3179,X3180)) ) ),
    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_451_zero__induct])])])])])]) ).

fof(i_0_1302,plain,
    ! [X3147] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3147))
      | X3147 = hAPP(nat,nat,suc,esk88_1(X3147)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_440_gr0__implies__Suc])])]) ).

fof(i_0_1303,plain,
    ! [X3086,X3088,X3089] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3086))
        | X3086 = hAPP(nat,nat,suc,esk84_1(X3086)) )
      & ( X3088 != hAPP(nat,nat,suc,X3089)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3088)) ) ),
    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_415_gr0__conv__Suc])])])])]) ).

fof(i_0_1304,plain,
    ( hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool))))
    & hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_461__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123])])]) ).

fof(i_0_1305,plain,
    ! [X2042,X2043,X2044] : hAPP(fun(X2042,fun(X2043,bool)),fun(fun(X2042,X2043),bool),hAPP(fun(X2042,bool),fun(fun(X2042,fun(X2043,bool)),fun(fun(X2042,X2043),bool)),pi(X2042,X2043),X2044),hAPP(fun(X2043,bool),fun(X2042,fun(X2043,bool)),combk(fun(X2043,bool),X2042),top_top(fun(X2043,bool)))) = top_top(fun(fun(X2042,X2043),bool)),
    inference(variable_rename,[status(thm)],[fact_88_Pi__UNIV]) ).

fof(i_0_1306,plain,
    ! [X2952] :
      ( ~ linordered_semidom(X2952)
      | ~ hBOOL(hAPP(X2952,bool,hAPP(X2952,fun(X2952,bool),ord_less_eq(X2952),one_one(X2952)),zero_zero(X2952))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_751])]) ).

fof(i_0_1307,plain,
    ! [X2954] :
      ( ~ linordered_semidom(X2954)
      | ~ hBOOL(hAPP(X2954,bool,hAPP(X2954,fun(X2954,bool),ord_less(X2954),one_one(X2954)),zero_zero(X2954))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_752])]) ).

fof(i_0_1308,plain,
    ! [X1893,X1894] :
      ( ~ top(X1893)
      | ~ hBOOL(hAPP(X1893,bool,hAPP(X1893,fun(X1893,bool),ord_less(X1893),top_top(X1893)),X1894)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_753])])]) ).

fof(i_0_1309,plain,
    ! [X3009] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X3009))),
    inference(variable_rename,[status(thm)],[fact_376_zero__less__Suc]) ).

fof(i_0_1310,plain,
    ! [X3006] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3006),hAPP(nat,nat,suc,X3006))),
    inference(variable_rename,[status(thm)],[fact_374_lessI]) ).

fof(i_0_1311,plain,
    ! [X1986,X1987] :
      ( ~ preorder(X1986)
      | ~ hBOOL(hAPP(X1986,bool,hAPP(X1986,fun(X1986,bool),ord_less(X1986),X1987),X1987)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_754])])]) ).

fof(i_0_1312,plain,
    ! [X2892] :
      ( ( X2892 = zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2892)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2892))
        | X2892 != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_323_neq0__conv])]) ).

fof(i_0_1313,plain,
    ! [X2900] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2900),zero_zero(nat)))
        | X2900 = zero_zero(nat) )
      & ( X2900 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2900),zero_zero(nat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_329_le__0__eq])]) ).

fof(i_0_1314,plain,
    ! [X2893] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2893),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[i_0_755]) ).

fof(i_0_1315,plain,
    ! [X2891] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2891),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[i_0_756]) ).

fof(i_0_1316,plain,
    ! [X2886] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2886),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[i_0_757]) ).

fof(i_0_1317,plain,
    ! [X2889,X2890] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2889),X2890))
      | X2890 != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_321_gr__implies__not0])]) ).

fof(i_0_1318,plain,
    ! [X2600,X2601] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2600),X2601))
      | X2600 != X2601 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_226_less__not__refl3])]) ).

fof(i_0_1319,plain,
    ! [X2598,X2599] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2598),X2599))
      | X2599 != X2598 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_225_less__not__refl2])]) ).

fof(i_0_1320,plain,
    ! [X2597] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2597),X2597)),
    inference(variable_rename,[status(thm)],[i_0_758]) ).

fof(i_0_1321,plain,
    ! [X2592] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2592),X2592)),
    inference(variable_rename,[status(thm)],[i_0_759]) ).

fof(i_0_1322,plain,
    ! [X2616,X2617,X2618] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2616),X2617) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2618),X2617)
        | X2616 = X2618 )
      & ( X2616 != X2618
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2616),X2617) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2618),X2617) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_232_nat__add__right__cancel])]) ).

fof(i_0_1323,plain,
    ! [X2613,X2614,X2615] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2613),X2614) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2613),X2615)
        | X2614 = X2615 )
      & ( X2614 != X2615
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2613),X2614) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2613),X2615) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_nat__add__left__cancel])]) ).

fof(i_0_1324,plain,
    ! [X3426,X3427] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X3426),X3427))
      | hBOOL(X3426)
      | hBOOL(X3427) ),
    inference(variable_rename,[status(thm)],[i_0_760]) ).

fof(i_0_1325,plain,
    ! [X3418,X3419] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X3418),X3419))
      | hBOOL(X3418) ),
    inference(variable_rename,[status(thm)],[i_0_761]) ).

fof(i_0_1326,plain,
    ! [X3420,X3421] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X3420),X3421))
      | hBOOL(X3421) ),
    inference(variable_rename,[status(thm)],[i_0_762]) ).

cnf(i_0_1327,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
    | ti(X1,X2) != ti(X1,X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_741]) ).

cnf(i_0_1328,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ti(X1,X2) != ti(X1,X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_744]) ).

cnf(i_0_1329,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_710]) ).

cnf(i_0_1330,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_687]) ).

cnf(i_0_1331,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X2)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_687]) ).

cnf(i_0_1332,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_763]) ).

cnf(i_0_1333,plain,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_764]) ).

cnf(i_0_1334,plain,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = ti(X1,X3),
    inference(split_conjunct,[status(thm)],[i_0_765]) ).

cnf(i_0_1335,plain,
    ti(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_766]) ).

cnf(i_0_1336,plain,
    ( ti(fun(X1,bool),X2) = top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool))) ),
    inference(split_conjunct,[status(thm)],[i_0_767]) ).

fof(i_0_1337,plain,
    ! [X2809,X2810] :
      ( ~ hBOOL(hAPP(fun(fun(X2809,X2810),bool),bool,finite_finite_1(fun(X2809,X2810)),top_top(fun(fun(X2809,X2810),bool))))
      | hBOOL(hAPP(fun(X2810,bool),bool,finite_finite_1(X2810),top_top(fun(X2810,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_299_finite__fun__UNIVD2])]) ).

fof(i_0_1338,plain,
    ! [X2314,X2315] : hBOOL(hAPP(fun(X2314,bool),bool,hAPP(fun(X2314,bool),fun(fun(X2314,bool),bool),ord_less_eq(fun(X2314,bool)),X2315),top_top(fun(X2314,bool)))),
    inference(variable_rename,[status(thm)],[fact_158_subset__UNIV]) ).

cnf(i_0_1339,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_768]) ).

fof(i_0_1340,plain,
    ! [X3084,X3085] :
      ( ( X3084 = zero_zero(nat)
        | X3084 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3084),X3085) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X3085 = hAPP(nat,nat,suc,zero_zero(nat))
        | X3084 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3084),X3085) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X3084 = zero_zero(nat)
        | X3085 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3084),X3085) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X3085 = hAPP(nat,nat,suc,zero_zero(nat))
        | X3085 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3084),X3085) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X3084 != hAPP(nat,nat,suc,zero_zero(nat))
        | X3085 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3084),X3085) = hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X3084 != zero_zero(nat)
        | X3085 != hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3084),X3085) = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_414_add__is__1])])]) ).

fof(i_0_1341,plain,
    ! [X3082,X3083] :
      ( ( X3082 = zero_zero(nat)
        | X3082 = 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),X3082),X3083) )
      & ( X3083 = hAPP(nat,nat,suc,zero_zero(nat))
        | X3082 = 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),X3082),X3083) )
      & ( X3082 = zero_zero(nat)
        | X3083 = zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3082),X3083) )
      & ( X3083 = hAPP(nat,nat,suc,zero_zero(nat))
        | X3083 = zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3082),X3083) )
      & ( X3082 != hAPP(nat,nat,suc,zero_zero(nat))
        | X3083 != zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3082),X3083) )
      & ( X3082 != zero_zero(nat)
        | X3083 != 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),X3082),X3083) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_413_one__is__add])])]) ).

fof(i_0_1342,plain,
    ! [X2525,X2526] : hBOOL(hAPP(fun(X2525,bool),bool,hAPP(fun(X2525,bool),fun(fun(X2525,bool),bool),ord_less_eq(fun(X2525,bool)),X2526),X2526)),
    inference(variable_rename,[status(thm)],[fact_207_subset__refl]) ).

cnf(i_0_1343,hypothesis,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
    inference(split_conjunct,[status(thm)],[tsy_v_F_res]) ).

cnf(i_0_1344,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omktop_res]) ).

cnf(i_0_1345,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omkbot_res]) ).

cnf(i_0_1346,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ti(X1,X2) != top_top(X1)
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_750]) ).

fof(i_0_1347,plain,
    ! [X2227,X2228] : hBOOL(hAPP(fun(X2227,bool),bool,hAPP(fun(X2227,X2227),fun(fun(X2227,bool),bool),inj_on(X2227,X2227),combi(X2227)),X2228)),
    inference(variable_rename,[status(thm)],[fact_139_inj__on__id2]) ).

fof(i_0_1348,plain,
    ! [X1882,X1883] : hBOOL(hAPP(fun(X1882,bool),bool,hAPP(X1882,fun(fun(X1882,bool),bool),member(X1882),X1883),top_top(fun(X1882,bool)))),
    inference(variable_rename,[status(thm)],[fact_27_iso__tuple__UNIV__I]) ).

fof(i_0_1349,plain,
    ! [X1880,X1881] : hBOOL(hAPP(fun(X1880,bool),bool,hAPP(X1880,fun(fun(X1880,bool),bool),member(X1880),X1881),top_top(fun(X1880,bool)))),
    inference(variable_rename,[status(thm)],[fact_26_UNIV__I]) ).

cnf(i_0_1350,plain,
    ( ti(X1,X3) = zero_zero(X1)
    | ti(X1,X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)
    | ~ semiri456707255roduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_769]) ).

fof(i_0_1351,plain,
    ! [X3097] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X3097)),
    inference(variable_rename,[status(thm)],[fact_418_inj__Suc]) ).

cnf(i_0_1352,plain,
    ( ti(X1,X2) = top_top(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1)))
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_748]) ).

fof(i_0_1353,plain,
    ! [X3251] :
      ( ~ ring_1(X3251)
      | hBOOL(hAPP(fun(X3251,bool),bool,hAPP(X3251,fun(fun(X3251,bool),bool),member(X3251),zero_zero(X3251)),ring_1_Ints(X3251))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_474_Ints__0])]) ).

fof(i_0_1354,plain,
    ! [X3252] :
      ( ~ ring_1(X3252)
      | hBOOL(hAPP(fun(X3252,bool),bool,hAPP(X3252,fun(fun(X3252,bool),bool),member(X3252),one_one(X3252)),ring_1_Ints(X3252))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_475_Ints__1])]) ).

fof(i_0_1355,plain,
    ! [X2804] :
      ( ( ~ hBOOL(hAPP(fun(option(X2804),bool),bool,finite_finite_1(option(X2804)),top_top(fun(option(X2804),bool))))
        | hBOOL(hAPP(fun(X2804,bool),bool,finite_finite_1(X2804),top_top(fun(X2804,bool)))) )
      & ( ~ hBOOL(hAPP(fun(X2804,bool),bool,finite_finite_1(X2804),top_top(fun(X2804,bool))))
        | hBOOL(hAPP(fun(option(X2804),bool),bool,finite_finite_1(option(X2804)),top_top(fun(option(X2804),bool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_296_finite__option__UNIV])]) ).

cnf(i_0_1356,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),product_prod_rec(X1,X2,X3)) = product_prod_rec(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_770]) ).

cnf(i_0_1357,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_771]) ).

cnf(i_0_1358,plain,
    ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_772]) ).

fof(i_0_1359,plain,
    ! [X2951] :
      ( ~ linordered_semidom(X2951)
      | hBOOL(hAPP(X2951,bool,hAPP(X2951,fun(X2951,bool),ord_less_eq(X2951),zero_zero(X2951)),one_one(X2951))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_351_zero__le__one])]) ).

fof(i_0_1360,plain,
    ! [X2953] :
      ( ~ linordered_semidom(X2953)
      | hBOOL(hAPP(X2953,bool,hAPP(X2953,fun(X2953,bool),ord_less(X2953),zero_zero(X2953)),one_one(X2953))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_353_zero__less__one])]) ).

cnf(i_0_1361,plain,
    ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),hilbert_inv_into(X1,X2)) = hilbert_inv_into(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_773]) ).

fof(i_0_1362,plain,
    ! [X3106,X3107,X3108] :
      ( ~ comm_semiring_1(X3106)
      | hAPP(X3106,X3106,hAPP(X3106,fun(X3106,X3106),plus_plus(X3106),X3107),X3108) = hAPP(X3106,X3106,hAPP(X3106,fun(X3106,X3106),plus_plus(X3106),X3108),X3107) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).

fof(i_0_1363,plain,
    ! [X2185,X2186] :
      ( ~ top(X2185)
      | hBOOL(hAPP(X2185,bool,hAPP(X2185,fun(X2185,bool),ord_less_eq(X2185),X2186),top_top(X2185))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_130_top__greatest])])]) ).

fof(i_0_1364,plain,
    ! [X2860,X2861] : hAPP(fun(X2860,bool),fun(sum_sum(X2861,X2860),bool),hAPP(fun(X2861,bool),fun(fun(X2860,bool),fun(sum_sum(X2861,X2860),bool)),sum_Plus(X2861,X2860),top_top(fun(X2861,bool))),top_top(fun(X2860,bool))) = top_top(fun(sum_sum(X2861,X2860),bool)),
    inference(variable_rename,[status(thm)],[fact_311_UNIV__Plus__UNIV]) ).

fof(i_0_1365,plain,
    ! [X2101,X2102,X2103] :
      ( ~ preorder(X2101)
      | X2102 != X2103
      | hBOOL(hAPP(X2101,bool,hAPP(X2101,fun(X2101,bool),ord_less_eq(X2101),X2102),X2103)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_105_order__eq__refl])])]) ).

fof(i_0_1366,plain,
    ! [X2049,X2050] :
      ( ~ preorder(X2049)
      | hBOOL(hAPP(X2049,bool,hAPP(X2049,fun(X2049,bool),ord_less_eq(X2049),X2050),X2050)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_90_order__refl])])]) ).

fof(i_0_1367,plain,
    ! [X2888] :
      ( X2888 = zero_zero(nat)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_320_gr0I])]) ).

fof(i_0_1368,plain,
    ! [X2901] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X2901)),
    inference(variable_rename,[status(thm)],[fact_330_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_1369,plain,
    ! [X2887] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X2887)),
    inference(variable_rename,[status(thm)],[fact_319_le0]) ).

cnf(i_0_1370,plain,
    ti(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),in_rel(X1,X2)) = in_rel(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_774]) ).

fof(i_0_1371,plain,
    ! [X2622,X2623] :
      ( X2622 != X2623
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2622),X2623)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_235_eq__imp__le])]) ).

fof(i_0_1372,plain,
    ! [X2619] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2619),X2619)),
    inference(variable_rename,[status(thm)],[fact_233_le__refl]) ).

fof(i_0_1373,plain,
    ! [X2605,X2606] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2605),X2606) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2606),X2605),
    inference(variable_rename,[status(thm)],[fact_228_nat__add__commute]) ).

fof(i_0_1374,plain,
    ! [X3416,X3417] :
      ( ~ hBOOL(X3417)
      | ~ hBOOL(X3416)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X3417),X3416)) ),
    inference(variable_rename,[status(thm)],[i_0_775]) ).

fof(i_0_1375,plain,
    ! [X3422,X3423] :
      ( ~ hBOOL(X3423)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X3423),X3422)) ),
    inference(variable_rename,[status(thm)],[i_0_776]) ).

fof(i_0_1376,plain,
    ! [X3424,X3425] :
      ( ~ hBOOL(X3425)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X3424),X3425)) ),
    inference(variable_rename,[status(thm)],[i_0_777]) ).

cnf(i_0_1377,plain,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_778]) ).

cnf(i_0_1378,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_779]) ).

cnf(i_0_1379,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | zero_zero(X1) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_780]) ).

cnf(i_0_1380,plain,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OProf_res]) ).

cnf(i_0_1381,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X2) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[i_0_781]) ).

cnf(i_0_1382,plain,
    ( ti(X1,X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
    | ti(X1,X2) != zero_zero(X1)
    | ~ semiri456707255roduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_769]) ).

fof(i_0_1383,plain,
    ! [X2896,X2897] :
      ( ( X2896 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2896),X2897) != zero_zero(nat) )
      & ( X2897 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2896),X2897) != zero_zero(nat) )
      & ( X2896 != zero_zero(nat)
        | X2897 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2896),X2897) = zero_zero(nat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_327_add__is__0])])]) ).

fof(i_0_1384,plain,
    ! [X2898,X2899] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2898),X2899) != X2898
      | X2899 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_328_add__eq__self__zero])]) ).

cnf(i_0_1385,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_779]) ).

cnf(i_0_1386,plain,
    ( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
    | ti(X1,X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_780]) ).

cnf(i_0_1387,plain,
    hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_782]) ).

cnf(i_0_1388,plain,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),bool)),inj_on(X1,X2)) = inj_on(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_783]) ).

cnf(i_0_1389,plain,
    hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_784]) ).

cnf(i_0_1390,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_785]) ).

cnf(i_0_1391,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_786]) ).

cnf(i_0_1392,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_787]) ).

cnf(i_0_1393,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_788]) ).

cnf(i_0_1394,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_789]) ).

cnf(i_0_1395,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_790]) ).

fof(i_0_1396,plain,
    ! [X3164] : hAPP(nat,nat,suc,X3164) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X3164),
    inference(variable_rename,[status(thm)],[fact_444_Suc__eq__plus1__left]) ).

fof(i_0_1397,plain,
    ! [X3165] : hAPP(nat,nat,suc,X3165) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3165),one_one(nat)),
    inference(variable_rename,[status(thm)],[fact_445_Suc__eq__plus1]) ).

fof(i_0_1398,plain,
    ! [X3104] : hAPP(nat,fun(nat,bool),ord_less(nat),X3104) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X3104)),
    inference(variable_rename,[status(thm)],[fact_425_less__eq__Suc__le__raw]) ).

cnf(i_0_1399,plain,
    ti(fun(X1,fun(X2,product_prod(X1,X2))),product_Pair(X1,X2)) = product_Pair(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_791]) ).

cnf(i_0_1400,plain,
    ti(X1,ti(X1,X2)) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_792]) ).

cnf(i_0_1401,plain,
    hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_793]) ).

cnf(i_0_1402,plain,
    ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_794]) ).

fof(i_0_1403,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(fof_simplification,[status(thm)],[fact_304_infinite__UNIV__nat]) ).

cnf(i_0_1404,plain,
    ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
    inference(split_conjunct,[status(thm)],[i_0_795]) ).

cnf(i_0_1405,plain,
    ( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_796]) ).

cnf(i_0_1406,plain,
    ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
    inference(split_conjunct,[status(thm)],[i_0_797]) ).

fof(i_0_1407,plain,
    ! [X1988] : top_top(fun(X1988,bool)) = hAPP(fun(X1988,bool),fun(X1988,bool),collect(X1988),hAPP(bool,fun(X1988,bool),combk(bool,X1988),fTrue)),
    inference(variable_rename,[status(thm)],[fact_74_UNIV__def]) ).

cnf(i_0_1408,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OLin_res]) ).

cnf(i_0_1409,hypothesis,
    ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
    inference(split_conjunct,[status(thm)],[tsy_v_P_____res]) ).

fof(i_0_1410,plain,
    ! [X2957,X2958] :
      ( hBOOL(hAPP(fun(X2957,bool),bool,finite_finite_1(X2957),X2958))
      | hAPP(fun(X2957,bool),nat,finite_card(X2957),X2958) = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_798])]) ).

fof(i_0_1411,plain,
    ! [X2894] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X2894) = X2894,
    inference(variable_rename,[status(thm)],[fact_325_plus__nat_Oadd__0]) ).

cnf(i_0_1412,hypothesis,
    ( hBOOL(X1)
    | ~ hBOOL(ti(bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_799]) ).

fof(i_0_1413,plain,
    ! [X2895] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2895),zero_zero(nat)) = X2895,
    inference(variable_rename,[status(thm)],[fact_326_Nat_Oadd__0__right]) ).

fof(i_0_1414,plain,
    ! [X3389] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X3389))
      | ~ hBOOL(X3389) ),
    inference(variable_rename,[status(thm)],[i_0_800]) ).

fof(i_0_1415,plain,
    ! [X3025,X3026] :
      ( ( hAPP(nat,nat,suc,X3025) != hAPP(nat,nat,suc,X3026)
        | X3025 = X3026 )
      & ( X3025 != X3026
        | hAPP(nat,nat,suc,X3025) = hAPP(nat,nat,suc,X3026) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_385_nat_Oinject])]) ).

fof(i_0_1416,plain,
    ! [X3023,X3024] :
      ( hAPP(nat,nat,suc,X3023) != hAPP(nat,nat,suc,X3024)
      | X3023 = X3024 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_384_Suc__inject])]) ).

cnf(i_0_1417,plain,
    ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
    inference(split_conjunct,[status(thm)],[i_0_801]) ).

fof(i_0_1418,plain,
    ! [X2799] :
      ( ~ finite_finite(X2799)
      | hBOOL(hAPP(fun(X2799,bool),bool,finite_finite_1(X2799),top_top(fun(X2799,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_293_finite__UNIV])]) ).

cnf(i_0_1419,plain,
    hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[i_0_802]) ).

cnf(i_0_1420,plain,
    ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_803]) ).

fof(i_0_1421,plain,
    ! [X1878,X1879] : hBOOL(hAPP(X1878,bool,top_top(fun(X1878,bool)),X1879)),
    inference(variable_rename,[status(thm)],[fact_25_top1I]) ).

cnf(i_0_1422,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_804]) ).

cnf(i_0_1423,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ ab_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_805]) ).

cnf(i_0_1424,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_806]) ).

fof(i_0_1425,plain,
    ! [X2787,X2788] :
      ( ~ finite_finite(X2787)
      | hBOOL(hAPP(fun(X2787,bool),bool,finite_finite_1(X2787),X2788)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_287_finite__code])])]) ).

fof(i_0_1426,plain,
    ! [X2785,X2786] :
      ( ~ finite_finite(X2785)
      | hBOOL(hAPP(fun(X2785,bool),bool,finite_finite_1(X2785),X2786)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_286_finite])])]) ).

cnf(i_0_1427,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_807]) ).

cnf(i_0_1428,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_808]) ).

cnf(i_0_1429,plain,
    ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
    inference(split_conjunct,[status(thm)],[i_0_809]) ).

cnf(i_0_1430,plain,
    ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
    inference(split_conjunct,[status(thm)],[i_0_810]) ).

cnf(i_0_1431,plain,
    ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
    inference(split_conjunct,[status(thm)],[i_0_811]) ).

cnf(i_0_1432,hypothesis,
    ( hBOOL(ti(bool,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_799]) ).

cnf(i_0_1433,plain,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
    inference(split_conjunct,[status(thm)],[tsy_v_Lba_____res]) ).

cnf(i_0_1434,plain,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
    inference(split_conjunct,[status(thm)],[tsy_v_Lab_____res]) ).

cnf(i_0_1435,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(split_conjunct,[status(thm)],[tsy_c_fdisj_res]) ).

cnf(i_0_1436,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(split_conjunct,[status(thm)],[tsy_c_fconj_res]) ).

cnf(i_0_1437,plain,
    ( ti(bool,X1) = fTrue
    | ti(bool,X1) = fFalse ),
    inference(split_conjunct,[status(thm)],[i_0_812]) ).

cnf(i_0_1438,plain,
    ( ti(bool,X1) = fTrue
    | ti(bool,X1) = fFalse ),
    inference(split_conjunct,[status(thm)],[i_0_813]) ).

fof(i_0_1439,plain,
    ! [X3390] :
      ( hBOOL(X3390)
      | hBOOL(hAPP(bool,bool,fNot,X3390)) ),
    inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).

fof(i_0_1440,plain,
    ! [X3101] : hAPP(nat,nat,suc,X3101) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[fact_422_Suc__not__Zero]) ).

fof(i_0_1441,plain,
    ! [X3100] : hAPP(nat,nat,suc,X3100) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[fact_421_nat_Osimps_I3_J]) ).

fof(i_0_1442,plain,
    ! [X3098] : hAPP(nat,nat,suc,X3098) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[fact_419_Suc__neq__Zero]) ).

fof(i_0_1443,plain,
    ! [X3103] : zero_zero(nat) != hAPP(nat,nat,suc,X3103),
    inference(variable_rename,[status(thm)],[fact_424_Zero__not__Suc]) ).

fof(i_0_1444,plain,
    ! [X3102] : zero_zero(nat) != hAPP(nat,nat,suc,X3102),
    inference(variable_rename,[status(thm)],[fact_423_nat_Osimps_I2_J]) ).

fof(i_0_1445,plain,
    ! [X3099] : zero_zero(nat) != hAPP(nat,nat,suc,X3099),
    inference(variable_rename,[status(thm)],[fact_420_Zero__neq__Suc]) ).

fof(i_0_1446,plain,
    ! [X3027] : hAPP(nat,nat,suc,X3027) != X3027,
    inference(variable_rename,[status(thm)],[fact_386_Suc__n__not__n]) ).

fof(i_0_1447,plain,
    ! [X3028] : X3028 != hAPP(nat,nat,suc,X3028),
    inference(variable_rename,[status(thm)],[fact_387_n__not__Suc__n]) ).

cnf(i_0_1448,plain,
    ti(fun(X1,X1),combi(X1)) = combi(X1),
    inference(split_conjunct,[status(thm)],[i_0_814]) ).

cnf(i_0_1449,plain,
    ( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
    | ~ ring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_815]) ).

cnf(i_0_1450,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(split_conjunct,[status(thm)],[tsy_c_Nat_OSuc_res]) ).

cnf(i_0_1451,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(split_conjunct,[status(thm)],[tsy_c_fNot_res]) ).

cnf(i_0_1452,plain,
    ti(fun(arrow_660593299e_indi,nat),h) = h,
    inference(split_conjunct,[status(thm)],[tsy_v_h_____res]) ).

fof(i_0_1453,plain,
    ! [X1890,X1891,X1892] :
      ( ~ top(X1891)
      | hAPP(X1890,X1891,top_top(fun(X1890,X1891)),X1892) = top_top(X1891) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_top__apply])])]) ).

cnf(i_0_1454,plain,
    ( ti(X1,top_top(X1)) = top_top(X1)
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_816]) ).

cnf(i_0_1455,plain,
    ( ti(X1,zero_zero(X1)) = zero_zero(X1)
    | ~ zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_817]) ).

cnf(i_0_1456,plain,
    ( ti(X1,one_one(X1)) = one_one(X1)
    | ~ one(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_818]) ).

cnf(i_0_1457,plain,
    ti(X1,undefined(X1)) = undefined(X1),
    inference(split_conjunct,[status(thm)],[i_0_819]) ).

fof(i_0_1458,plain,
    ! [X3177] :
      ( X3177 = zero_zero(nat)
      | X3177 = hAPP(nat,nat,suc,esk96_1(X3177)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_450_nat_Oexhaust])])]) ).

fof(i_0_1459,plain,
    ! [X3175] :
      ( X3175 = zero_zero(nat)
      | X3175 = hAPP(nat,nat,suc,esk95_1(X3175)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_449_not0__implies__Suc])])]) ).

cnf(i_0_1460,plain,
    ti(nat,n) = n,
    inference(split_conjunct,[status(thm)],[tsy_v_n_____res]) ).

cnf(i_0_1461,plain,
    ti(bool,fTrue) = fTrue,
    inference(split_conjunct,[status(thm)],[tsy_c_fTrue_res]) ).

cnf(i_0_1462,plain,
    ti(bool,fFalse) = fFalse,
    inference(split_conjunct,[status(thm)],[tsy_c_fFalse_res]) ).

cnf(i_0_1463,plain,
    ti(arrow_490897120le_alt,e) = e,
    inference(split_conjunct,[status(thm)],[tsy_v_e_____res]) ).

cnf(i_0_1464,hypothesis,
    ti(arrow_490897120le_alt,d) = d,
    inference(split_conjunct,[status(thm)],[tsy_v_d_____res]) ).

cnf(i_0_1465,hypothesis,
    ti(arrow_490897120le_alt,c) = c,
    inference(split_conjunct,[status(thm)],[tsy_v_c_____res]) ).

cnf(i_0_1466,plain,
    ti(arrow_490897120le_alt,b) = b,
    inference(split_conjunct,[status(thm)],[tsy_v_b_____res]) ).

cnf(i_0_1467,plain,
    ti(arrow_490897120le_alt,a) = a,
    inference(split_conjunct,[status(thm)],[tsy_v_a_____res]) ).

fof(i_0_1468,plain,
    ! [X3375,X3376] :
      ( ~ finite_finite(X3376)
      | ~ finite_finite(X3375)
      | finite_finite(sum_sum(X3375,X3376)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum___Finite__Set_Ofinite])]) ).

fof(i_0_1469,plain,
    ! [X3367,X3368] :
      ( ~ finite_finite(X3368)
      | ~ finite_finite(X3367)
      | finite_finite(fun(X3367,X3368)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Finite__Set_Ofinite])]) ).

fof(i_0_1470,plain,
    ! [X3378,X3379] :
      ( ~ finite_finite(X3379)
      | ~ finite_finite(X3378)
      | finite_finite(product_prod(X3378,X3379)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod___Finite__Set_Ofinite])]) ).

fof(i_0_1471,plain,
    ! [X3369,X3370] :
      ( ~ order(X3370)
      | order(fun(X3369,X3370)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oorder])]) ).

fof(i_0_1472,plain,
    ! [X3365,X3366] :
      ( ~ preorder(X3366)
      | preorder(fun(X3365,X3366)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Opreorder])]) ).

fof(i_0_1473,plain,
    ! [X3371,X3372] :
      ( ~ top(X3372)
      | top(fun(X3371,X3372)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Otop])]) ).

fof(i_0_1474,plain,
    ! [X3373,X3374] :
      ( ~ ord(X3374)
      | ord(fun(X3373,X3374)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oord])]) ).

fof(i_0_1475,plain,
    ! [X2905] :
      ( ~ zero_neq_one(X2905)
      | one_one(X2905) != zero_zero(X2905) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_333_one__neq__zero])]) ).

fof(i_0_1476,plain,
    ! [X2904] :
      ( ~ zero_neq_one(X2904)
      | zero_zero(X2904) != one_one(X2904) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_332_zero__neq__one])]) ).

fof(i_0_1477,plain,
    ! [X3377] :
      ( ~ finite_finite(X3377)
      | finite_finite(option(X3377)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option_Ooption___Finite__Set_Ofinite])]) ).

cnf(i_0_1478,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_820]),
    [final] ).

cnf(i_0_1479,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_821]),
    [final] ).

cnf(i_0_1480,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_822]),
    [final] ).

cnf(i_0_1481,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    inference(split_conjunct,[status(thm)],[i_0_820]),
    [final] ).

cnf(i_0_1482,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    inference(split_conjunct,[status(thm)],[i_0_821]),
    [final] ).

cnf(i_0_1483,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ),
    inference(split_conjunct,[status(thm)],[i_0_822]),
    [final] ).

cnf(i_0_1484,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    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_1485,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    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_1486,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    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_1487,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_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_1488,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),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_823]),
    [final] ).

cnf(i_0_1489,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),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_824]),
    [final] ).

cnf(i_0_1490,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    inference(split_conjunct,[status(thm)],[fact_80_n_I3_J]),
    [final] ).

cnf(i_0_1491,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk28_0)) ),
    inference(split_conjunct,[status(thm)],[i_0_823]),
    [final] ).

cnf(i_0_1492,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk27_0)) ),
    inference(split_conjunct,[status(thm)],[i_0_824]),
    [final] ).

cnf(i_0_1493,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),n)) ),
    inference(split_conjunct,[status(thm)],[i_0_825]),
    [final] ).

cnf(i_0_1494,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba)),arrow_1111136790e_Prof)),
    inference(split_conjunct,[status(thm)],[i_0_826]),
    [final] ).

cnf(i_0_1495,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_827]),
    [final] ).

cnf(i_0_1496,plain,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_827]),
    [final] ).

cnf(i_0_1497,plain,
    ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2)))))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_828]),
    [final] ).

cnf(i_0_1498,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1))
    | hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) ),
    inference(split_conjunct,[status(thm)],[i_0_829]),
    [final] ).

cnf(i_0_1499,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X4)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk43_6(X2,X1,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk42_6(X2,X1,X4,X3,X5,X6))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X5)),X6))
    | ~ order(X1)
    | ~ order(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_830]),
    [final] ).

cnf(i_0_1500,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X4)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,esk41_6(X2,X1,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk40_6(X2,X1,X4,X3,X5,X6))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X5)),X6))
    | ~ order(X1)
    | ~ ord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_831]),
    [final] ).

cnf(i_0_1501,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X5)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk48_6(X2,X1,X3,X4,X5,X6))),hAPP(X2,X1,X3,esk49_6(X2,X1,X3,X4,X5,X6))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X6)),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ order(X1)
    | ~ order(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_832]),
    [final] ).

cnf(i_0_1502,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,X5)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,esk58_6(X2,X1,X3,X4,X5,X6))),hAPP(X2,X1,X3,esk59_6(X2,X1,X3,X4,X5,X6))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X6)),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ order(X1)
    | ~ order(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_833]),
    [final] ).

cnf(i_0_1503,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),hAPP(X2,X1,X3,X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk57_6(X1,X2,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk56_6(X1,X2,X4,X3,X5,X6))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),hAPP(X2,X1,X3,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ order(X2)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_834]),
    [final] ).

cnf(i_0_1504,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),hAPP(X2,X1,X3,X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,esk55_6(X1,X2,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk54_6(X1,X2,X4,X3,X5,X6))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),hAPP(X2,X1,X3,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ order(X2)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_835]),
    [final] ).

cnf(i_0_1505,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X3,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk46_6(X1,X2,X4,X5,X3,X6))),hAPP(X2,X1,X3,esk47_6(X1,X2,X4,X5,X3,X6))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X6),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X3,X6)))
    | ~ order(X2)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_836]),
    [final] ).

cnf(i_0_1506,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X3,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X3,esk44_6(X1,X2,X4,X5,X3,X6))),hAPP(X2,X1,X3,esk45_6(X1,X2,X4,X5,X3,X6))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X6),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X3,X6)))
    | ~ order(X2)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_837]),
    [final] ).

cnf(i_0_1507,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_838,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1508,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_840,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1509,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X6)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X6)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X6)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X6)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_841,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1510,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_842,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1511,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_843,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1512,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_844,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1513,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_845,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1514,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X6)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X6)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X6)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X6)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_846,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1515,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_847,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1516,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_848,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1517,plain,
    ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1))
    | hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_849]),
    [final] ).

cnf(i_0_1518,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1519,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X1,X2)),esk25_2(X1,X2))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk23_2(X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_628]),
    [final] ).

cnf(i_0_1520,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1521,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1522,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1523,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1524,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X1,X2)),esk25_2(X1,X2))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk23_2(X1,X2),X1)))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2),X1))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_628]),
    [final] ).

cnf(i_0_1525,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk23_2(X1,X2)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2),X1))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_628]),
    [final] ).

cnf(i_0_1526,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk9_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk9_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1527,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk9_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk9_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1528,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_853,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1529,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_854,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1530,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X2),X1))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),esk25_2(X1,X2)) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),esk24_2(X1,X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_855,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1531,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1532,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1533,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_856]),
    [final] ).

cnf(i_0_1534,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X3)),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_856]),
    [final] ).

cnf(i_0_1535,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1536,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1537,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1538,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1539,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1540,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(cn,[status(thm)],[i_0_857]),
    [final] ).

cnf(i_0_1541,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1542,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk9_5(X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk9_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1543,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk9_5(X3,X5,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk9_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1544,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk3_5(X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_858,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1545,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X3,X5,X2,X4,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk3_5(X3,X5,X2,X4,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_859,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1546,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_860,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1547,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_861,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1548,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk48_6(X1,X2,X3,X4,X5,X6)),esk49_6(X1,X2,X3,X4,X5,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X5)),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
    | ~ order(X2)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_832]),
    [final] ).

cnf(i_0_1549,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk58_6(X1,X2,X3,X4,X5,X6)),esk59_6(X1,X2,X3,X4,X5,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X5)),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X6)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
    | ~ order(X2)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_833]),
    [final] ).

cnf(i_0_1550,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk43_6(X1,X2,X3,X4,X5,X6)),esk42_6(X1,X2,X3,X4,X5,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X4,X3)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X4,X5)),X6))
    | ~ order(X2)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_830]),
    [final] ).

cnf(i_0_1551,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk41_6(X1,X2,X3,X4,X5,X6)),esk40_6(X1,X2,X3,X4,X5,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X4,X3)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X4,X5)),X6))
    | ~ order(X2)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_831]),
    [final] ).

cnf(i_0_1552,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))),
    inference(split_conjunct,[status(thm)],[i_0_862]),
    [final] ).

cnf(i_0_1553,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk57_6(X2,X1,X3,X4,X5,X6)),esk56_6(X2,X1,X3,X4,X5,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),hAPP(X1,X2,X4,X6)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),hAPP(X1,X2,X4,X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
    | ~ order(X1)
    | ~ order(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_834]),
    [final] ).

cnf(i_0_1554,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk55_6(X2,X1,X3,X4,X5,X6)),esk54_6(X2,X1,X3,X4,X5,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),hAPP(X1,X2,X4,X6)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),hAPP(X1,X2,X4,X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
    | ~ order(X1)
    | ~ order(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_835]),
    [final] ).

cnf(i_0_1555,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk46_6(X2,X1,X3,X4,X5,X6)),esk47_6(X2,X1,X3,X4,X5,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),hAPP(X1,X2,X5,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X3))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),hAPP(X1,X2,X5,X6)))
    | ~ order(X1)
    | ~ order(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_836]),
    [final] ).

cnf(i_0_1556,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk44_6(X2,X1,X3,X4,X5,X6)),esk45_6(X2,X1,X3,X4,X5,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),hAPP(X1,X2,X5,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X3))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X4),hAPP(X1,X2,X5,X6)))
    | ~ order(X1)
    | ~ order(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_837]),
    [final] ).

cnf(i_0_1557,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1558,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1559,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X5),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_863,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1560,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_864,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1561,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1562,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X3,X4,X2,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X3,X4,X2,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_865,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1563,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_866,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1564,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1565,plain,
    ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(fun(X2,X1),bool),fun(fun(fun(X2,X1),bool),bool),ord_less_eq(fun(fun(X2,X1),bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X5),X3)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X5),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X2,fun(X1,bool),X3,esk52_5(X1,X2,X3,X4,X5))),hAPP(X2,fun(X1,bool),X4,esk52_5(X1,X2,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_867]),
    [final] ).

cnf(i_0_1566,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1567,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1568,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X6),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk67_6(X2,X1,X5,X3,X6,X4)),X4))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_868]),
    [final] ).

cnf(i_0_1569,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X6),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk67_6(X2,X1,X5,X6,X3,X4)),X4))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_868]),
    [final] ).

cnf(i_0_1570,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1571,plain,
    ( hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),combi(fun(product_prod(X1,X2),bool)),X3) = hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),combi(fun(product_prod(X1,X2),bool)),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))),X4))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_869,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1572,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_856]),
    [final] ).

cnf(i_0_1573,plain,
    hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
    inference(split_conjunct,[status(thm)],[fact_32_assms_I1_J]),
    [final] ).

cnf(i_0_1574,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1575,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1576,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1577,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_870]),
    [final] ).

cnf(i_0_1578,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3)),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_870]),
    [final] ).

cnf(i_0_1579,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X2)),X1))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk77_2(X1,X2)),hAPP(nat,nat,X2,esk77_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_871]),
    [final] ).

cnf(i_0_1580,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e))) ),
    inference(cn,[status(thm)],[i_0_872]),
    [final] ).

cnf(i_0_1581,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1582,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X3)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_873,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1583,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X5))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_874,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1584,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X5),X4)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_875,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1585,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_876,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1586,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_877,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1587,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_878,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1588,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X5),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X5),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_879,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1589,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X5),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_880,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1590,plain,
    ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X5),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk68_5(X1,X2,X3,X4,X5))),hAPP(X2,fun(X1,bool),X4,esk68_5(X1,X2,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_881]),
    [final] ).

cnf(i_0_1591,plain,
    ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X5),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk33_5(X1,X2,X3,X4,X5))),hAPP(X2,fun(X1,bool),X4,esk33_5(X1,X2,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_882]),
    [final] ).

cnf(i_0_1592,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X6),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hAPP(X1,X2,X3,esk67_6(X2,X1,X5,X3,X6,X4)) != hAPP(X1,X2,X6,esk67_6(X2,X1,X5,X3,X6,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_868]),
    [final] ).

cnf(i_0_1593,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X6),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hAPP(X1,X2,X6,esk67_6(X2,X1,X5,X6,X3,X4)) != hAPP(X1,X2,X3,esk67_6(X2,X1,X5,X6,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_868]),
    [final] ).

cnf(i_0_1594,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1595,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ linordered_idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_883]),
    [final] ).

cnf(i_0_1596,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1597,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_884,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1598,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X3)),X5))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_885,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1599,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1600,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1601,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X2),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_886,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1602,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X5),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_887,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1603,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X3),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_888,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1604,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_889,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1605,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1606,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1607,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_629]),
    [final] ).

cnf(i_0_1608,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1609,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(cn,[status(thm)],[i_0_890]),
    [final] ).

cnf(i_0_1610,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1611,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1612,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1613,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1614,plain,
    ( hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(fun(X1,bool),X2,X6,X8)),hAPP(fun(X1,bool),X2,X6,X7)) = hAPP(fun(X1,bool),X2,X6,X7)
    | ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_891]),
    [final] ).

cnf(i_0_1615,plain,
    ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X5),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X4))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk65_5(X1,X2,X3,X4,X5))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_892]),
    [final] ).

cnf(i_0_1616,plain,
    ( hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(X1,X2,X5,X8)),hAPP(fun(X1,bool),X2,X6,X7)) = hAPP(fun(X1,bool),X2,X6,X7)
    | ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X7))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X8),X7)) ),
    inference(split_conjunct,[status(thm)],[i_0_893]),
    [final] ).

cnf(i_0_1617,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_894,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1618,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_895,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1619,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_896,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1620,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X3)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_897,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1621,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_898,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1622,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X5),X4)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_899,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1623,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X4) = hAPP(fun(X2,bool),nat,finite_card(X2),X5)
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X6),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X5),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X4))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X6),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_900]),
    [final] ).

cnf(i_0_1624,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_901,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1625,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X5),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_902,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1626,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X3),X2)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_903,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1627,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_904,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1628,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1629,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1630,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(cn,[status(thm)],[i_0_905]),
    [final] ).

cnf(i_0_1631,plain,
    ( hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),combi(fun(product_prod(X1,X2),bool)),X3) = hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),combi(fun(product_prod(X1,X2),bool)),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))),X4))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X3,X4)),esk22_4(X1,X2,X3,X4))),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_906,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1632,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1633,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X4),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_907,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1634,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X5)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X4),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_908,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1635,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_850]),
    [final] ).

cnf(i_0_1636,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk14_4(X1,X2,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_909]),
    [final] ).

cnf(i_0_1637,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(cn,[status(thm)],[i_0_910]),
    [final] ).

cnf(i_0_1638,plain,
    ( hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,X7),X7) = hAPP(X2,X2,combi(X2),X7)
    | ~ hBOOL(hAPP(fun(fun(X1,bool),X2),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool),hAPP(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool)),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(X1,X2),fun(fun(fun(X1,bool),X2),bool))),finite908156982e_idem(X2,X1),X3),X4),X5),X6)) ),
    inference(rw,[status(thm)],[i_0_911,c_0_839]),
    [final] ).

cnf(i_0_1639,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1640,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_851]),
    [final] ).

cnf(i_0_1641,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
    inference(cn,[status(thm)],[i_0_912]),
    [final] ).

cnf(i_0_1642,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ linordered_idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_883]),
    [final] ).

cnf(i_0_1643,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_913,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1644,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_914,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1645,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_915]),
    [final] ).

cnf(i_0_1646,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(cn,[status(thm)],[i_0_916]),
    [final] ).

cnf(i_0_1647,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk10_1(X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk11_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1648,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_917,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1649,plain,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_918]),
    [final] ).

cnf(i_0_1650,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_919]),
    [final] ).

cnf(i_0_1651,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),hAPP(fun(X2,X1),fun(X2,X4),hAPP(fun(X1,X4),fun(fun(X2,X1),fun(X2,X4)),combb(X1,X4,X2),X5),X3)),top_top(fun(X2,bool)))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),top_top(fun(X2,bool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_920]),
    [final] ).

cnf(i_0_1652,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk52_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),X3)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_867]),
    [final] ).

cnf(i_0_1653,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_921,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1654,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_922,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1655,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X5),X2),X4)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_923,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1656,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X5),X4),X2)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X5),arrow_2064824852le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_924,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1657,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X5),X4),X2)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_925]),
    [final] ).

cnf(i_0_1658,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk61_3(X2,X3,X1))),hAPP(nat,nat,X1,esk62_3(X2,X3,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_926]),
    [final] ).

cnf(i_0_1659,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,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_1660,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk91_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_927]),
    [final] ).

cnf(i_0_1661,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_928,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1662,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_929,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1663,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_930,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1664,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_931,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1665,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_932]),
    [final] ).

cnf(i_0_1666,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1667,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1668,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_933]),
    [final] ).

cnf(i_0_1669,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,esk89_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk89_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_934]),
    [final] ).

cnf(i_0_1670,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk90_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk90_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_935]),
    [final] ).

cnf(i_0_1671,plain,
    ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X4,X1)),hAPP(nat,X3,X4,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X4,esk91_4(X3,X1,X2,X4))),hAPP(nat,X3,X4,hAPP(nat,nat,suc,esk91_4(X3,X1,X2,X4)))))
    | ~ order(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_927]),
    [final] ).

cnf(i_0_1672,plain,
    ( X1 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1))))) ),
    inference(split_conjunct,[status(thm)],[i_0_936]),
    [final] ).

cnf(i_0_1673,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X6))
    | hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),combi(fun(product_prod(X1,X2),bool)),X5) != hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),combi(fun(product_prod(X1,X2),bool)),X6)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_937,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1674,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X6))
    | hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),combi(fun(product_prod(X1,X2),bool)),X5) != hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),combi(fun(product_prod(X1,X2),bool)),X6)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_938,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1675,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X4)),hAPP(fun(X2,bool),nat,finite_card(X2),X5)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_939]),
    [final] ).

cnf(i_0_1676,plain,
    ( hAPP(X1,X1,combi(X1),X5) = hAPP(X1,X1,combi(X1),X6)
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X5) != hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X4),X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_940,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1677,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_941]),
    [final] ).

cnf(i_0_1678,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_942,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1679,plain,
    ( hBOOL(hAPP(fun(fun(X1,X4),bool),bool,hAPP(fun(fun(X1,X4),bool),fun(fun(fun(X1,X4),bool),bool),ord_less_eq(fun(fun(X1,X4),bool)),hAPP(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool)),pi(X1,X4),X3),X5)),hAPP(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool)),pi(X1,X4),X2),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_943]),
    [final] ).

cnf(i_0_1680,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_919]),
    [final] ).

cnf(i_0_1681,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk10_1(X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk11_1(X1))))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1682,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk61_3(X1,X2,X3)),esk62_3(X1,X2,X3)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_926]),
    [final] ).

cnf(i_0_1683,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_944,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1684,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_945,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1685,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk65_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_892]),
    [final] ).

cnf(i_0_1686,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_946,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1687,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_947,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1688,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X3)))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_948]),
    [final] ).

cnf(i_0_1689,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5)))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_948]),
    [final] ).

cnf(i_0_1690,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2))),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_949]),
    [final] ).

cnf(i_0_1691,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X3),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X3),X2)),X2)) ),
    inference(rw,[status(thm)],[i_0_950,c_0_839]),
    [final] ).

cnf(i_0_1692,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,bool),fun(fun(X4,bool),bool),ord_less_eq(fun(X4,bool)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_933]),
    [final] ).

cnf(i_0_1693,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,X6)),hAPP(X1,fun(X2,bool),X5,X6)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_951]),
    [final] ).

cnf(i_0_1694,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,X6)),hAPP(X1,fun(X2,bool),X5,X6)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_952]),
    [final] ).

cnf(i_0_1695,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),esk102_5(X2,X1,X3,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X3),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_647]),
    [final] ).

cnf(i_0_1696,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_953]),
    [final] ).

cnf(i_0_1697,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_954]),
    [final] ).

cnf(i_0_1698,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk101_5(X2,X1,X3,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_649]),
    [final] ).

cnf(i_0_1699,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),in_rel(X1,X2),X5),X3),X4))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_955]),
    [final] ).

cnf(i_0_1700,plain,
    ( hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite_1(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_956]),
    [final] ).

cnf(i_0_1701,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk68_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_881]),
    [final] ).

cnf(i_0_1702,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk33_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_882]),
    [final] ).

cnf(i_0_1703,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,fun(X4,X2)),fun(fun(X1,bool),bool),inj_on(X1,fun(X4,X2)),hAPP(fun(X1,X2),fun(X1,fun(X4,X2)),hAPP(fun(X2,fun(X4,X2)),fun(fun(X1,X2),fun(X1,fun(X4,X2))),combb(X2,fun(X4,X2),X1),combk(X2,X4)),X3)),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_957]),
    [final] ).

cnf(i_0_1704,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk15_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_909]),
    [final] ).

cnf(i_0_1705,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_958]),
    [final] ).

cnf(i_0_1706,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_959]),
    [final] ).

cnf(i_0_1707,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_960]),
    [final] ).

cnf(i_0_1708,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_961]),
    [final] ).

cnf(i_0_1709,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_962]),
    [final] ).

cnf(i_0_1710,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_963]),
    [final] ).

cnf(i_0_1711,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_964]),
    [final] ).

cnf(i_0_1712,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_965]),
    [final] ).

cnf(i_0_1713,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_966]),
    [final] ).

cnf(i_0_1714,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_967]),
    [final] ).

cnf(i_0_1715,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,bool),fun(fun(X4,bool),bool),ord_less_eq(fun(X4,bool)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X2)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_968]),
    [final] ).

cnf(i_0_1716,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_969]),
    [final] ).

cnf(i_0_1717,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_970]),
    [final] ).

cnf(i_0_1718,plain,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk39_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk39_4(X2,X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_971]),
    [final] ).

cnf(i_0_1719,plain,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk29_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk29_4(X2,X1,X3,X4))))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_972]),
    [final] ).

cnf(i_0_1720,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    inference(split_conjunct,[status(thm)],[i_0_973]),
    [final] ).

cnf(i_0_1721,plain,
    ( hBOOL(hAPP(fun(product_prod(X2,X1),bool),bool,hAPP(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),member(product_prod(X2,X1)),hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X4),X5)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),in_rel(X2,X1),X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_955]),
    [final] ).

cnf(i_0_1722,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X1)),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_974]),
    [final] ).

cnf(i_0_1723,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X5),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk71_5(X2,X1,X3,X5,X4)),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_975]),
    [final] ).

cnf(i_0_1724,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X5),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk71_5(X2,X1,X5,X3,X4)),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_975]),
    [final] ).

cnf(i_0_1725,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X4),X2)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_976,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1726,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X4),X2)))
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) != hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_977,c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1727,plain,
    ( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X2)
    | ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_978]),
    [final] ).

cnf(i_0_1728,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)))
    | ~ ordere779506340up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_979]),
    [final] ).

cnf(i_0_1729,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)))
    | ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_980]),
    [final] ).

cnf(i_0_1730,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)))
    | ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_981]),
    [final] ).

cnf(i_0_1731,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)))
    | ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_982]),
    [final] ).

cnf(i_0_1732,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk63_3(X2,X3,X1))),hAPP(nat,nat,X1,esk64_3(X2,X3,X1))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_983]),
    [final] ).

cnf(i_0_1733,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_984]),
    [final] ).

cnf(i_0_1734,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_985]),
    [final] ).

cnf(i_0_1735,plain,
    ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3)),X4)) = hAPP(fun(X2,bool),fun(X2,bool),combi(fun(X2,bool)),X4)
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),top_top(fun(X1,bool))) != top_top(fun(X2,bool)) ),
    inference(rw,[status(thm)],[i_0_986,c_0_839]),
    [final] ).

cnf(i_0_1736,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_954]),
    [final] ).

cnf(i_0_1737,plain,
    ( hAPP(X3,X1,X4,hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X5),X4),X2)) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(rw,[status(thm)],[i_0_987,c_0_839]),
    [final] ).

cnf(i_0_1738,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    inference(split_conjunct,[status(thm)],[i_0_988]),
    [final] ).

cnf(i_0_1739,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    inference(split_conjunct,[status(thm)],[i_0_989]),
    [final] ).

cnf(i_0_1740,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_990]),
    [final] ).

cnf(i_0_1741,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_991]),
    [final] ).

cnf(i_0_1742,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linordered_idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_992]),
    [final] ).

cnf(i_0_1743,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk102_5(X1,X3,X2,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(rw,[status(thm)],[i_0_993,c_0_839]),
    [final] ).

cnf(i_0_1744,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),ring_1_Ints(X1)))
    | ~ ring_1(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_994]),
    [final] ).

cnf(i_0_1745,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_995]),
    [final] ).

cnf(i_0_1746,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_996]),
    [final] ).

cnf(i_0_1747,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_996]),
    [final] ).

cnf(i_0_1748,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_997]),
    [final] ).

cnf(i_0_1749,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_998]),
    [final] ).

cnf(i_0_1750,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_999]),
    [final] ).

cnf(i_0_1751,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere779506340up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1000]),
    [final] ).

cnf(i_0_1752,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_960]),
    [final] ).

cnf(i_0_1753,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere779506340up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1001]),
    [final] ).

cnf(i_0_1754,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_962]),
    [final] ).

cnf(i_0_1755,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_964]),
    [final] ).

cnf(i_0_1756,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1002]),
    [final] ).

cnf(i_0_1757,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_966]),
    [final] ).

cnf(i_0_1758,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1003]),
    [final] ).

cnf(i_0_1759,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,esk71_5(X2,X1,X3,X5,X4)) != hAPP(X1,X2,X5,esk71_5(X2,X1,X3,X5,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_975]),
    [final] ).

cnf(i_0_1760,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X5,esk71_5(X2,X1,X5,X3,X4)) != hAPP(X1,X2,X3,esk71_5(X2,X1,X5,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_975]),
    [final] ).

cnf(i_0_1761,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1004]),
    [final] ).

cnf(i_0_1762,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_969]),
    [final] ).

cnf(i_0_1763,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1005]),
    [final] ).

cnf(i_0_1764,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_970]),
    [final] ).

cnf(i_0_1765,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1006]),
    [final] ).

cnf(i_0_1766,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1007]),
    [final] ).

cnf(i_0_1767,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1008]),
    [final] ).

cnf(i_0_1768,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1009]),
    [final] ).

cnf(i_0_1769,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1010]),
    [final] ).

cnf(i_0_1770,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X3,X1,X4,esk101_5(X1,X3,X2,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(rw,[status(thm)],[i_0_1011,c_0_839]),
    [final] ).

cnf(i_0_1771,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk15_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_909]),
    [final] ).

cnf(i_0_1772,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1012,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1773,plain,
    hBOOL(hAPP(fun(fun(X1,X1),bool),bool,hAPP(fun(X1,X1),fun(fun(fun(X1,X1),bool),bool),member(fun(X1,X1)),combi(X1)),hAPP(fun(X1,fun(X1,bool)),fun(fun(X1,X1),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X1,bool)),fun(fun(X1,X1),bool)),pi(X1,X1),X2),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),combk(fun(X1,bool),X1),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_1013]),
    [final] ).

cnf(i_0_1774,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1014]),
    [final] ).

cnf(i_0_1775,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1015]),
    [final] ).

cnf(i_0_1776,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,bool),fun(fun(X4,bool),bool),ord_less_eq(fun(X4,bool)),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
    | hAPP(fun(X4,bool),fun(X4,bool),combi(fun(X4,bool)),X5) != hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_1016,c_0_839]),
    [final] ).

cnf(i_0_1777,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1017]),
    [final] ).

cnf(i_0_1778,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1018]),
    [final] ).

cnf(i_0_1779,plain,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1019]),
    [final] ).

cnf(i_0_1780,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_1020]),
    [final] ).

cnf(i_0_1781,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_1021]),
    [final] ).

cnf(i_0_1782,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1022]),
    [final] ).

cnf(i_0_1783,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1023]),
    [final] ).

cnf(i_0_1784,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_990]),
    [final] ).

cnf(i_0_1785,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_991]),
    [final] ).

cnf(i_0_1786,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linordered_idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_992]),
    [final] ).

cnf(i_0_1787,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1024]),
    [final] ).

cnf(i_0_1788,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite_1(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1025]),
    [final] ).

cnf(i_0_1789,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1025]),
    [final] ).

cnf(i_0_1790,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1026]),
    [final] ).

cnf(i_0_1791,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1027]),
    [final] ).

cnf(i_0_1792,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),esk26_2(X1,X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1028,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1793,plain,
    ( hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,esk50_4(X1,X2,X3,X4)),esk51_4(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1029]),
    [final] ).

cnf(i_0_1794,plain,
    ( hAPP(X1,X4,X5,X2) = hAPP(X1,X4,X5,X3)
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1030,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1795,plain,
    ( hAPP(X1,X1,combi(X1),X4) = hAPP(X1,X1,combi(X1),X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1031,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1796,plain,
    ( hAPP(X1,X1,combi(X1),X5) = hAPP(X1,X1,combi(X1),X6)
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1032,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1797,plain,
    ( hAPP(X1,X1,combi(X1),X5) = hAPP(X1,X1,combi(X1),X6)
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1033,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1798,plain,
    ( hAPP(X1,X1,combi(X1),X5) = hAPP(X1,X1,combi(X1),X6)
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1034,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1799,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk32_2(X1,X2)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_978]),
    [final] ).

cnf(i_0_1800,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X3,X1,X4,X5)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X6)) ),
    inference(rw,[status(thm)],[i_0_1035,c_0_839]),
    [final] ).

cnf(i_0_1801,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
    | hAPP(X4,X4,combi(X4),X5) != hAPP(X1,X4,X6,X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_1036,c_0_839]),
    [final] ).

cnf(i_0_1802,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),X5),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X6),X3)))
    | hAPP(X4,X4,combi(X4),X5) != hAPP(X1,X4,X6,X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_1037,c_0_839]),
    [final] ).

cnf(i_0_1803,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1038]),
    [final] ).

cnf(i_0_1804,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1039]),
    [final] ).

cnf(i_0_1805,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1040]),
    [final] ).

cnf(i_0_1806,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1041]),
    [final] ).

cnf(i_0_1807,plain,
    hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_1042]),
    [final] ).

cnf(i_0_1808,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1043]),
    [final] ).

cnf(i_0_1809,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1044]),
    [final] ).

cnf(i_0_1810,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1045]),
    [final] ).

cnf(i_0_1811,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1046]),
    [final] ).

cnf(i_0_1812,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ linordered_semidom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1047]),
    [final] ).

cnf(i_0_1813,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),esk99_3(X1,X2,X3))))
    | ~ linordered_field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1048]),
    [final] ).

cnf(i_0_1814,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),esk19_0)),
    inference(split_conjunct,[status(thm)],[i_0_1049]),
    [final] ).

cnf(i_0_1815,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
    inference(split_conjunct,[status(thm)],[fact_38__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]),
    [final] ).

cnf(i_0_1816,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),esk18_0)),
    inference(split_conjunct,[status(thm)],[i_0_1050]),
    [final] ).

cnf(i_0_1817,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
    inference(split_conjunct,[status(thm)],[fact_37__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]),
    [final] ).

cnf(i_0_1818,plain,
    hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)) = hAPP(fun(X4,bool),fun(X2,bool),hAPP(fun(X4,X2),fun(fun(X4,bool),fun(X2,bool)),image(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),combb(X1,X2,X4),X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[i_0_1051]),
    [final] ).

cnf(i_0_1819,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk38_4(X1,X2,X3,X4)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1052]),
    [final] ).

cnf(i_0_1820,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X4),X3),X6) = hAPP(X1,X1,combi(X1),X5)
    | hAPP(X1,X2,X3,X5) != hAPP(X2,X2,combi(X2),X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1053,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1821,plain,
    ( hBOOL(hAPP(product_prod(X1,X2),bool,X3,X4))
    | ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk7_3(X1,X2,X3)),esk8_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1054]),
    [final] ).

cnf(i_0_1822,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X4),X3),hAPP(X1,X2,X3,X5)) = hAPP(X1,X1,combi(X1),X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(rw,[status(thm)],[i_0_1055,c_0_839]),
    [final] ).

cnf(i_0_1823,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1056]),
    [final] ).

cnf(i_0_1824,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1057]),
    [final] ).

cnf(i_0_1825,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk63_3(X1,X2,X3)),esk64_3(X1,X2,X3)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X3,X1)),hAPP(nat,nat,X3,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_983]),
    [final] ).

cnf(i_0_1826,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X3),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1058]),
    [final] ).

cnf(i_0_1827,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X4,X5),X6))
    | ~ hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X3,X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1059]),
    [final] ).

cnf(i_0_1828,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1060]),
    [final] ).

cnf(i_0_1829,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1061]),
    [final] ).

cnf(i_0_1830,plain,
    ( hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3) = hAPP(fun(X2,X1),fun(X2,X1),combi(fun(X2,X1)),X4)
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,esk34_4(X1,X2,X4,X3))) != hAPP(X2,X2,combi(X2),esk34_4(X1,X2,X4,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1062,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1831,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1063]),
    [final] ).

cnf(i_0_1832,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1064]),
    [final] ).

cnf(i_0_1833,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1065]),
    [final] ).

cnf(i_0_1834,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1066]),
    [final] ).

cnf(i_0_1835,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1067]),
    [final] ).

cnf(i_0_1836,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1068]),
    [final] ).

cnf(i_0_1837,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1069]),
    [final] ).

cnf(i_0_1838,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1070]),
    [final] ).

cnf(i_0_1839,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1071]),
    [final] ).

cnf(i_0_1840,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),top_top(fun(X2,bool))))),
    inference(split_conjunct,[status(thm)],[i_0_1072]),
    [final] ).

cnf(i_0_1841,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1073]),
    [final] ).

cnf(i_0_1842,plain,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X5)
    | hAPP(X1,X1,combi(X1),X4) != hAPP(X1,X1,combi(X1),X5)
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1074,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1843,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1075,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1844,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1076,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1845,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1077,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1846,plain,
    ( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X5)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1078,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1847,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1079]),
    [final] ).

cnf(i_0_1848,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1080]),
    [final] ).

cnf(i_0_1849,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite_1(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1081]),
    [final] ).

cnf(i_0_1850,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite_1(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1025]),
    [final] ).

cnf(i_0_1851,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1082]),
    [final] ).

cnf(i_0_1852,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1083]),
    [final] ).

cnf(i_0_1853,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1084]),
    [final] ).

cnf(i_0_1854,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1085]),
    [final] ).

cnf(i_0_1855,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1086]),
    [final] ).

cnf(i_0_1856,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk15_1(X1)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_909]),
    [final] ).

cnf(i_0_1857,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk11_1(X1)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1858,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk10_1(X1)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_852]),
    [final] ).

cnf(i_0_1859,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5)))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1087]),
    [final] ).

cnf(i_0_1860,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5)))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1088]),
    [final] ).

cnf(i_0_1861,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X5)),hAPP(X1,X2,X4,X5)))
    | ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
    | ~ ord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_972]),
    [final] ).

cnf(i_0_1862,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1089]),
    [final] ).

cnf(i_0_1863,plain,
    hAPP(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),combi(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))))),finite908156982e_idem(X1,X2)) = finite908156982e_idem(X1,X2),
    inference(rw,[status(thm)],[i_0_1090,c_0_839]),
    [final] ).

cnf(i_0_1864,plain,
    ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X4),X3))
    | hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
    | ~ ord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1091]),
    [final] ).

cnf(i_0_1865,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,esk50_4(X1,X2,X4,X3)),esk51_4(X1,X2,X4,X3)))
    | hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1029]),
    [final] ).

cnf(i_0_1866,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk38_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1052]),
    [final] ).

cnf(i_0_1867,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1056]),
    [final] ).

cnf(i_0_1868,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1057]),
    [final] ).

cnf(i_0_1869,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),top_top(fun(X3,bool)))))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X3,X1,X4,X5) ),
    inference(rw,[status(thm)],[i_0_1092,c_0_839]),
    [final] ).

cnf(i_0_1870,plain,
    ( hAPP(fun(sum_sum(X1,X3),bool),nat,finite_card(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1093]),
    [final] ).

cnf(i_0_1871,plain,
    ( hAPP(fun(sum_sum(X1,X3),bool),nat,finite_card(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1094]),
    [final] ).

cnf(i_0_1872,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1095,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1873,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1096,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1874,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) != hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1097]),
    [final] ).

cnf(i_0_1875,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X4))
    | hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)) != hAPP(fun(X2,bool),nat,finite_card(X2),X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1098]),
    [final] ).

cnf(i_0_1876,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1024]),
    [final] ).

cnf(i_0_1877,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1024]),
    [final] ).

cnf(i_0_1878,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1099]),
    [final] ).

cnf(i_0_1879,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1100]),
    [final] ).

cnf(i_0_1880,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1101]),
    [final] ).

cnf(i_0_1881,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1102]),
    [final] ).

cnf(i_0_1882,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1103]),
    [final] ).

cnf(i_0_1883,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1104]),
    [final] ).

cnf(i_0_1884,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1105]),
    [final] ).

cnf(i_0_1885,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1106]),
    [final] ).

cnf(i_0_1886,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3),X5) = hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,X2,X3,X4) != hAPP(X2,X2,combi(X2),X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1107,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1887,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk94_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1108]),
    [final] ).

cnf(i_0_1888,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1109]),
    [final] ).

cnf(i_0_1889,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1110]),
    [final] ).

cnf(i_0_1890,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1111]),
    [final] ).

cnf(i_0_1891,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1112]),
    [final] ).

cnf(i_0_1892,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1113]),
    [final] ).

cnf(i_0_1893,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1069]),
    [final] ).

cnf(i_0_1894,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1071]),
    [final] ).

cnf(i_0_1895,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1114]),
    [final] ).

cnf(i_0_1896,plain,
    ( hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) = hAPP(fun(X1,bool),nat,finite_card(X1),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1098]),
    [final] ).

cnf(i_0_1897,plain,
    ( ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X4),X3))
    | ~ ord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1091]),
    [final] ).

cnf(i_0_1898,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3),hAPP(X1,X2,X3,X4)) = hAPP(X1,X1,combi(X1),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(rw,[status(thm)],[i_0_1115,c_0_839]),
    [final] ).

cnf(i_0_1899,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X3) != zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1116,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1900,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk38_4(X1,X3,X2,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1052]),
    [final] ).

cnf(i_0_1901,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(rw,[status(thm)],[i_0_1117,c_0_839]),
    [final] ).

cnf(i_0_1902,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) != zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(rw,[status(thm)],[i_0_1118,c_0_839]),
    [final] ).

cnf(i_0_1903,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1119]),
    [final] ).

cnf(i_0_1904,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1120]),
    [final] ).

cnf(i_0_1905,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1121]),
    [final] ).

cnf(i_0_1906,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1122]),
    [final] ).

cnf(i_0_1907,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1123]),
    [final] ).

cnf(i_0_1908,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1124]),
    [final] ).

cnf(i_0_1909,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1125]),
    [final] ).

cnf(i_0_1910,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1126]),
    [final] ).

cnf(i_0_1911,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
    inference(split_conjunct,[status(thm)],[fact_3__096P_A_058_AProf_096]),
    [final] ).

cnf(i_0_1912,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1127]),
    [final] ).

cnf(i_0_1913,plain,
    arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_138_Prof__def]),
    [final] ).

cnf(i_0_1914,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1128]),
    [final] ).

cnf(i_0_1915,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1129]),
    [final] ).

cnf(i_0_1916,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ ab_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1130]),
    [final] ).

cnf(i_0_1917,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1131]),
    [final] ).

cnf(i_0_1918,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1132]),
    [final] ).

cnf(i_0_1919,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1133]),
    [final] ).

cnf(i_0_1920,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_1134]),
    [final] ).

cnf(i_0_1921,plain,
    ( hAPP(nat,nat,suc,X1) = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1135]),
    [final] ).

cnf(i_0_1922,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1136,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1923,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1137,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1924,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1110]),
    [final] ).

cnf(i_0_1925,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1111]),
    [final] ).

cnf(i_0_1926,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1138]),
    [final] ).

cnf(i_0_1927,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1))) = hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1139]),
    [final] ).

cnf(i_0_1928,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1140]),
    [final] ).

cnf(i_0_1929,plain,
    ( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1141,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1930,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk70_4(X2,X1,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_719]),
    [final] ).

cnf(i_0_1931,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk69_4(X2,X1,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_719]),
    [final] ).

cnf(i_0_1932,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk31_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_658]),
    [final] ).

cnf(i_0_1933,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk30_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_658]),
    [final] ).

cnf(i_0_1934,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 = hAPP(nat,nat,suc,X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1142]),
    [final] ).

cnf(i_0_1935,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 = hAPP(nat,nat,suc,X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1143]),
    [final] ).

cnf(i_0_1936,plain,
    ( X1 = hAPP(nat,nat,suc,esk94_2(X2,X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1108]),
    [final] ).

cnf(i_0_1937,plain,
    ( X2 = hAPP(nat,nat,suc,esk92_2(X1,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1144]),
    [final] ).

cnf(i_0_1938,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk86_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1145]),
    [final] ).

cnf(i_0_1939,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1146]),
    [final] ).

cnf(i_0_1940,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1))) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1147]),
    [final] ).

cnf(i_0_1941,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk85_2(X1,X2)),X2))
    | X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1148]),
    [final] ).

cnf(i_0_1942,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk53_3(X1,X2,X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1149]),
    [final] ).

cnf(i_0_1943,plain,
    ( hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,esk6_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1054]),
    [final] ).

cnf(i_0_1944,plain,
    ( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk86_3(X1,X2,X3))))
    | hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1145]),
    [final] ).

cnf(i_0_1945,plain,
    ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X3),X4))
    | ~ ord(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1091]),
    [final] ).

cnf(i_0_1946,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1150]),
    [final] ).

cnf(i_0_1947,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1151]),
    [final] ).

cnf(i_0_1948,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1152]),
    [final] ).

cnf(i_0_1949,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1153]),
    [final] ).

cnf(i_0_1950,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1154]),
    [final] ).

cnf(i_0_1951,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1155]),
    [final] ).

cnf(i_0_1952,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1156,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1953,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1157,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1954,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1158,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1955,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1159,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1956,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1160]),
    [final] ).

cnf(i_0_1957,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1161]),
    [final] ).

cnf(i_0_1958,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_679]),
    [final] ).

cnf(i_0_1959,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_680]),
    [final] ).

cnf(i_0_1960,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X3)))
    | X1 != hAPP(nat,nat,suc,X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1148]),
    [final] ).

cnf(i_0_1961,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),esk73_1(X1)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1162]),
    [final] ).

cnf(i_0_1962,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),esk75_1(X1)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1163]),
    [final] ).

cnf(i_0_1963,plain,
    ( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk79_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_1164]),
    [final] ).

cnf(i_0_1964,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1089]),
    [final] ).

cnf(i_0_1965,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) != top_top(fun(X1,bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_1165]),
    [final] ).

cnf(i_0_1966,plain,
    ( hBOOL(X4)
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1166]),
    [final] ).

cnf(i_0_1967,plain,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1167]),
    [final] ).

cnf(i_0_1968,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1146]),
    [final] ).

cnf(i_0_1969,plain,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1168]),
    [final] ).

cnf(i_0_1970,plain,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1169]),
    [final] ).

cnf(i_0_1971,plain,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1170]),
    [final] ).

cnf(i_0_1972,plain,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1171]),
    [final] ).

cnf(i_0_1973,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1172]),
    [final] ).

cnf(i_0_1974,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1173]),
    [final] ).

cnf(i_0_1975,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1174]),
    [final] ).

cnf(i_0_1976,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_723]),
    [final] ).

cnf(i_0_1977,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1132]),
    [final] ).

cnf(i_0_1978,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1175]),
    [final] ).

cnf(i_0_1979,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1143]),
    [final] ).

cnf(i_0_1980,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1155]),
    [final] ).

cnf(i_0_1981,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1176]),
    [final] ).

cnf(i_0_1982,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1177]),
    [final] ).

cnf(i_0_1983,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1154]),
    [final] ).

cnf(i_0_1984,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1178]),
    [final] ).

cnf(i_0_1985,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1179]),
    [final] ).

cnf(i_0_1986,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1180,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1987,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1181,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1988,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X4)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1182,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1989,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1183,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1990,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1184,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1991,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X4)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1185,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_1992,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1186]),
    [final] ).

cnf(i_0_1993,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1187]),
    [final] ).

cnf(i_0_1994,plain,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,esk86_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1145]),
    [final] ).

cnf(i_0_1995,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk37_3(X1,X2,X3)),X2))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1188]),
    [final] ).

cnf(i_0_1996,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1189]),
    [final] ).

cnf(i_0_1997,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1190]),
    [final] ).

cnf(i_0_1998,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1191]),
    [final] ).

cnf(i_0_1999,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1192]),
    [final] ).

cnf(i_0_2000,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1193]),
    [final] ).

cnf(i_0_2001,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X1),X2))
    | X2 = X1
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2002,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_1195]),
    [final] ).

cnf(i_0_2003,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk32_2(X1,X2)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk32_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_978]),
    [final] ).

cnf(i_0_2004,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1196,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2005,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1197,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2006,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1198,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2007,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1199,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2008,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1200,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2009,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1201,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2010,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1202,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2011,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1203,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2012,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1204,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2013,plain,
    ( hAPP(X1,X4,X5,X2) = hAPP(X1,X4,X5,X3)
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),top_top(fun(X1,bool)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1205,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2014,plain,
    ( hAPP(X1,X1,combi(X1),X4) = hAPP(X1,X1,combi(X1),X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1206,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2015,plain,
    ( hAPP(X1,X1,combi(X1),X4) = hAPP(X1,X1,combi(X1),X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1207,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2016,plain,
    ( hBOOL(hAPP(nat,bool,X3,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk79_2(X2,X3)))
    | ~ hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1164]),
    [final] ).

cnf(i_0_2017,plain,
    ( hBOOL(hAPP(nat,bool,X3,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk81_2(X2,X3)))
    | ~ hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1208]),
    [final] ).

cnf(i_0_2018,plain,
    ( hBOOL(hAPP(X1,bool,X3,X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1209]),
    [final] ).

cnf(i_0_2019,plain,
    ( hBOOL(hAPP(X1,bool,X4,X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1210]),
    [final] ).

cnf(i_0_2020,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk72_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1211]),
    [final] ).

cnf(i_0_2021,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
    | ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1))) ),
    inference(rw,[status(thm)],[i_0_1212,c_0_839]),
    [final] ).

cnf(i_0_2022,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk26_2(X1,X2)),arrow_2064824852le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1213,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2023,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1214]),
    [final] ).

cnf(i_0_2024,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1215,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2025,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,X3),fun(X1,X2)),combs(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),hAPP(X1,X3,X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_1216]),
    [final] ).

cnf(i_0_2026,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X1,combi(X1),esk70_4(X2,X1,X3,X4)) != hAPP(X1,X1,combi(X1),esk69_4(X2,X1,X3,X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1217,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2027,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X1,combi(X1),esk31_4(X1,X2,X3,X4)) != hAPP(X1,X1,combi(X1),esk30_4(X1,X2,X3,X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1218,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2028,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk53_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1149]),
    [final] ).

cnf(i_0_2029,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk93_2(X1,X2)))
    | X2 = hAPP(nat,nat,suc,X1)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1219]),
    [final] ).

cnf(i_0_2030,plain,
    ( X2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk87_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1220]),
    [final] ).

cnf(i_0_2031,plain,
    ( X2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk83_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1214]),
    [final] ).

cnf(i_0_2032,plain,
    ( X1 = hAPP(nat,nat,suc,esk85_2(X1,X2))
    | X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1148]),
    [final] ).

cnf(i_0_2033,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_710]),
    [final] ).

cnf(i_0_2034,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_711]),
    [final] ).

cnf(i_0_2035,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1221]),
    [final] ).

cnf(i_0_2036,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1146]),
    [final] ).

cnf(i_0_2037,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1))) ),
    inference(rw,[status(thm)],[i_0_1222,c_0_839]),
    [final] ).

cnf(i_0_2038,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1153]),
    [final] ).

cnf(i_0_2039,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1133]),
    [final] ).

cnf(i_0_2040,plain,
    hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),combi(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool))),arrow_218898985ctator) = arrow_218898985ctator,
    inference(rw,[status(thm)],[i_0_1223,c_0_839]),
    [final] ).

cnf(i_0_2041,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_1224]),
    [final] ).

cnf(i_0_2042,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk82_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1225]),
    [final] ).

cnf(i_0_2043,plain,
    hAPP(fun(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)))),fun(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)))),combi(fun(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))))),finite_fold_image(nat,X1)) = finite_fold_image(nat,X1),
    inference(rw,[status(thm)],[i_0_1226,c_0_839]),
    [final] ).

cnf(i_0_2044,plain,
    hAPP(product_prod(X1,X2),X3,hAPP(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3),product_prod_rec(X1,X2,X3),X4),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X4,X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_1227]),
    [final] ).

cnf(i_0_2045,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1228]),
    [final] ).

cnf(i_0_2046,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1229]),
    [final] ).

cnf(i_0_2047,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1230]),
    [final] ).

cnf(i_0_2048,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1231]),
    [final] ).

cnf(i_0_2049,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1232]),
    [final] ).

cnf(i_0_2050,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1233]),
    [final] ).

cnf(i_0_2051,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1229]),
    [final] ).

cnf(i_0_2052,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1230]),
    [final] ).

cnf(i_0_2053,plain,
    ( X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1234]),
    [final] ).

cnf(i_0_2054,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1235,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2055,plain,
    hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),combi(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),arrow_831799591nimity) = arrow_831799591nimity,
    inference(rw,[status(thm)],[i_0_1236,c_0_839]),
    [final] ).

cnf(i_0_2056,plain,
    hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),combi(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    inference(rw,[status(thm)],[i_0_1237,c_0_839]),
    [final] ).

cnf(i_0_2057,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1238]),
    [final] ).

cnf(i_0_2058,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk66_0),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_1239]),
    [final] ).

cnf(i_0_2059,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk19_0),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_1049]),
    [final] ).

cnf(i_0_2060,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk18_0),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_1050]),
    [final] ).

cnf(i_0_2061,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_35__096Lba_A_058_ALin_096]),
    [final] ).

cnf(i_0_2062,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_34__096Lab_A_058_ALin_096]),
    [final] ).

cnf(i_0_2063,plain,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk98_2(X2,X1))))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1240]),
    [final] ).

cnf(i_0_2064,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linordered_idom(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1241,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2065,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1242,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2066,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1243,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2067,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1244,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2068,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1245,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2069,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1246,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2070,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1247,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2071,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(sum_sum(X1,X3),bool),nat,finite_card(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)) = zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1093]),
    [final] ).

cnf(i_0_2072,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2)) = zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1093]),
    [final] ).

cnf(i_0_2073,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk37_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1188]),
    [final] ).

cnf(i_0_2074,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_1248]),
    [final] ).

cnf(i_0_2075,plain,
    hAPP(X1,X2,hAPP(X3,fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),X5),
    inference(split_conjunct,[status(thm)],[i_0_1249]),
    [final] ).

cnf(i_0_2076,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X1,product_prod(X4,X1),hAPP(X4,fun(X1,product_prod(X4,X1)),product_Pair(X4,X1),X5),X2) != hAPP(X1,product_prod(X4,X1),hAPP(X4,fun(X1,product_prod(X4,X1)),product_Pair(X4,X1),X6),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1250,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2077,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X1,product_prod(X4,X1),hAPP(X4,fun(X1,product_prod(X4,X1)),product_Pair(X4,X1),X5),X2) != hAPP(X1,product_prod(X4,X1),hAPP(X4,fun(X1,product_prod(X4,X1)),product_Pair(X4,X1),X6),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1251,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2078,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X2),X5) != hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X3),X6) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1252,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2079,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X2),X5) != hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X3),X6) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1253,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2080,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_1254]),
    [final] ).

cnf(i_0_2081,plain,
    ( hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X2),X5) = hAPP(X4,product_prod(X1,X4),hAPP(X1,fun(X4,product_prod(X1,X4)),product_Pair(X1,X4),X3),X6)
    | hAPP(X4,X4,combi(X4),X5) != hAPP(X4,X4,combi(X4),X6)
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1255,c_0_839]),c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2082,plain,
    ( hAPP(X1,X2,X3,esk69_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,esk70_4(X2,X1,X3,X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_719]),
    [final] ).

cnf(i_0_2083,plain,
    ( hAPP(X1,X2,X3,esk30_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,esk31_4(X1,X2,X3,X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_658]),
    [final] ).

cnf(i_0_2084,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),esk99_3(X1,X2,X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linordered_field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1048]),
    [final] ).

cnf(i_0_2085,plain,
    hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combi(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),arrow_1322701812_below) = arrow_1322701812_below,
    inference(rw,[status(thm)],[i_0_1256,c_0_839]),
    [final] ).

cnf(i_0_2086,plain,
    hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combi(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),arrow_14103264_above) = arrow_14103264_above,
    inference(rw,[status(thm)],[i_0_1257,c_0_839]),
    [final] ).

cnf(i_0_2087,plain,
    ( hBOOL(hAPP(X1,bool,X3,X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1258]),
    [final] ).

cnf(i_0_2088,plain,
    ( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1259,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2089,plain,
    ( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1260,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2090,plain,
    ( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1261,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2091,plain,
    ( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1262,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2092,plain,
    ( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1263,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2093,plain,
    ( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1264,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2094,plain,
    ( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1265,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2095,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk82_2(X1,X2)) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1225]),
    [final] ).

cnf(i_0_2096,plain,
    ( X2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk60_2(X1,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1266]),
    [final] ).

cnf(i_0_2097,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X1,combi(X1),esk36_3(X1,X2,X3)) != hAPP(X1,X1,combi(X1),esk35_3(X1,X2,X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1267,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2098,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1268]),
    [final] ).

cnf(i_0_2099,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1269]),
    [final] ).

cnf(i_0_2100,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1270]),
    [final] ).

cnf(i_0_2101,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1174]),
    [final] ).

cnf(i_0_2102,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1271]),
    [final] ).

cnf(i_0_2103,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1272]),
    [final] ).

cnf(i_0_2104,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1172]),
    [final] ).

cnf(i_0_2105,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1273,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2106,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1274,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2107,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1275,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2108,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1276,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2109,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1277,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2110,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1278,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2111,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1279,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2112,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk74_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1162]),
    [final] ).

cnf(i_0_2113,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk76_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1163]),
    [final] ).

cnf(i_0_2114,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk78_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1280]),
    [final] ).

cnf(i_0_2115,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1281]),
    [final] ).

cnf(i_0_2116,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,finite_finite_1(product_prod(X1,X2)),top_top(fun(product_prod(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1282]),
    [final] ).

cnf(i_0_2117,plain,
    hAPP(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),combi(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)))),pi(X1,X2)) = pi(X1,X2),
    inference(rw,[status(thm)],[i_0_1283,c_0_839]),
    [final] ).

cnf(i_0_2118,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1284]),
    [final] ).

cnf(i_0_2119,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1285]),
    [final] ).

cnf(i_0_2120,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1286]),
    [final] ).

cnf(i_0_2121,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk80_2(X1,X2)),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1287]),
    [final] ).

cnf(i_0_2122,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_1288]),
    [final] ).

cnf(i_0_2123,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1289,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2124,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1290,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2125,plain,
    ( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
    | ~ cancel146912293up_add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1291,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2126,plain,
    ( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
    | ~ cancel_semigroup_add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1292,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2127,plain,
    ( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
    | ~ cancel_semigroup_add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1293,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2128,plain,
    ( hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3) = hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X4)
    | hAPP(X1,X2,X3,esk20_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk20_4(X1,X2,X3,X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1294,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2129,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1295,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2130,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_1296]),
    [final] ).

cnf(i_0_2131,plain,
    ( X1 = hAPP(nat,nat,suc,esk93_2(X2,X1))
    | X1 = hAPP(nat,nat,suc,X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1219]),
    [final] ).

cnf(i_0_2132,plain,
    ( hAPP(X1,X1,combi(X1),X2) != top_top(X1)
    | ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1))) ),
    inference(rw,[status(thm)],[i_0_1297,c_0_839]),
    [final] ).

cnf(i_0_2133,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk81_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_1208]),
    [final] ).

cnf(i_0_2134,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk79_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_1164]),
    [final] ).

cnf(i_0_2135,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1143]),
    [final] ).

cnf(i_0_2136,plain,
    ( hAPP(fun(X2,bool),nat,finite_card(X2),top_top(fun(X2,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1298]),
    [final] ).

cnf(i_0_2137,plain,
    ( hAPP(X1,X2,X3,esk35_3(X1,X2,X3)) = hAPP(X1,X2,X3,esk36_3(X1,X2,X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_732]),
    [final] ).

cnf(i_0_2138,plain,
    ( hAPP(X1,X1,combi(X1),X2) = top_top(X1)
    | ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2)) ),
    inference(rw,[status(thm)],[i_0_1299,c_0_839]),
    [final] ).

cnf(i_0_2139,plain,
    ( hAPP(X1,X1,combi(X1),X2) = top_top(X1)
    | ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2)) ),
    inference(rw,[status(thm)],[i_0_1300,c_0_839]),
    [final] ).

cnf(i_0_2140,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[i_0_823]),
    [final] ).

cnf(i_0_2141,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk27_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[i_0_824]),
    [final] ).

cnf(i_0_2142,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[fact_19_n_I1_J]),
    [final] ).

cnf(i_0_2143,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1266]),
    [final] ).

cnf(i_0_2144,plain,
    ( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk97_1(X1))))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1301]),
    [final] ).

cnf(i_0_2145,plain,
    ( X1 = hAPP(nat,nat,suc,esk88_1(X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1302]),
    [final] ).

cnf(i_0_2146,plain,
    ( X1 = hAPP(nat,nat,suc,esk84_1(X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1303]),
    [final] ).

cnf(i_0_2147,plain,
    hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_1304]),
    [final] ).

cnf(i_0_2148,plain,
    hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[fact_456_surjh]),
    [final] ).

cnf(i_0_2149,plain,
    hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),top_top(fun(X2,bool)))) = top_top(fun(fun(X1,X2),bool)),
    inference(split_conjunct,[status(thm)],[i_0_1305]),
    [final] ).

cnf(i_0_2150,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1258]),
    [final] ).

cnf(i_0_2151,plain,
    ( ~ linordered_semidom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1306]),
    [final] ).

cnf(i_0_2152,plain,
    ( ~ linordered_semidom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1307]),
    [final] ).

cnf(i_0_2153,plain,
    ( ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1308]),
    [final] ).

cnf(i_0_2154,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat))))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1234]),
    [final] ).

cnf(i_0_2155,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_1309]),
    [final] ).

cnf(i_0_2156,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1148]),
    [final] ).

cnf(i_0_2157,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1154]),
    [final] ).

cnf(i_0_2158,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
    inference(split_conjunct,[status(thm)],[i_0_1310]),
    [final] ).

cnf(i_0_2159,plain,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1311]),
    [final] ).

cnf(i_0_2160,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1312]),
    [final] ).

cnf(i_0_2161,plain,
    ( X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1313]),
    [final] ).

cnf(i_0_2162,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[i_0_1314]),
    [final] ).

cnf(i_0_2163,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[i_0_1315]),
    [final] ).

cnf(i_0_2164,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[i_0_1316]),
    [final] ).

cnf(i_0_2165,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1317]),
    [final] ).

cnf(i_0_2166,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1230]),
    [final] ).

cnf(i_0_2167,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1318]),
    [final] ).

cnf(i_0_2168,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_1319]),
    [final] ).

cnf(i_0_2169,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1285]),
    [final] ).

cnf(i_0_2170,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_1285]),
    [final] ).

cnf(i_0_2171,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1320]),
    [final] ).

cnf(i_0_2172,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1321]),
    [final] ).

cnf(i_0_2173,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_1322]),
    [final] ).

cnf(i_0_2174,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_1323]),
    [final] ).

cnf(i_0_2175,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1324]),
    [final] ).

cnf(i_0_2176,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1325]),
    [final] ).

cnf(i_0_2177,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1326]),
    [final] ).

cnf(i_0_2178,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk76_2(X1,X2)),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1163]),
    [final] ).

cnf(i_0_2179,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk74_2(X1,X2)),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1162]),
    [final] ).

cnf(i_0_2180,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk78_2(X1,X2)),X2))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1280]),
    [final] ).

cnf(i_0_2181,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1327,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2182,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1328,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2183,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1329,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2184,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1330,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2185,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ order(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1331,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2186,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1332,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2187,plain,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = hAPP(X1,X1,combi(X1),X2),
    inference(rw,[status(thm)],[i_0_1333,c_0_839]),
    [final] ).

cnf(i_0_2188,plain,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = hAPP(X1,X1,combi(X1),X3),
    inference(rw,[status(thm)],[i_0_1334,c_0_839]),
    [final] ).

cnf(i_0_2189,plain,
    hAPP(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),combi(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
    inference(rw,[status(thm)],[i_0_1335,c_0_839]),
    [final] ).

cnf(i_0_2190,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = top_top(fun(X1,bool))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(rw,[status(thm)],[i_0_1336,c_0_839]),
    [final] ).

cnf(i_0_2191,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1281]),
    [final] ).

cnf(i_0_2192,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(X2,X1),bool),bool,finite_finite_1(sum_sum(X2,X1)),top_top(fun(sum_sum(X2,X1),bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1281]),
    [final] ).

cnf(i_0_2193,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1337]),
    [final] ).

cnf(i_0_2194,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_1338]),
    [final] ).

cnf(i_0_2195,plain,
    hAPP(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combi(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3)))),combs(X1,X2,X3)) = combs(X1,X2,X3),
    inference(rw,[status(thm)],[i_0_1339,c_0_839]),
    [final] ).

cnf(i_0_2196,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_1340]),
    [final] ).

cnf(i_0_2197,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_1341]),
    [final] ).

cnf(i_0_2198,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1342]),
    [final] ).

cnf(i_0_2199,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,esk97_1(X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1301]),
    [final] ).

cnf(i_0_2200,hypothesis,
    hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combi(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f) = f,
    inference(rw,[status(thm)],[i_0_1343,c_0_839]),
    [final] ).

cnf(i_0_2201,plain,
    hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combi(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    inference(rw,[status(thm)],[i_0_1344,c_0_839]),
    [final] ).

cnf(i_0_2202,plain,
    hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combi(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    inference(rw,[status(thm)],[i_0_1345,c_0_839]),
    [final] ).

cnf(i_0_2203,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | hAPP(X1,X1,combi(X1),X2) != top_top(X1)
    | ~ top(X1) ),
    inference(rw,[status(thm)],[i_0_1346,c_0_839]),
    [final] ).

cnf(i_0_2204,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1347]),
    [final] ).

cnf(i_0_2205,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_1304]),
    [final] ).

cnf(i_0_2206,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[fact_20_injh]),
    [final] ).

cnf(i_0_2207,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1303]),
    [final] ).

cnf(i_0_2208,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_1348]),
    [final] ).

cnf(i_0_2209,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_1349]),
    [final] ).

cnf(i_0_2210,plain,
    ( hAPP(X1,X1,combi(X1),X3) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1350,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2211,plain,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1351]),
    [final] ).

cnf(i_0_2212,plain,
    ( hAPP(X1,X1,combi(X1),X2) = top_top(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1)))
    | ~ top(X1) ),
    inference(rw,[status(thm)],[i_0_1352,c_0_839]),
    [final] ).

cnf(i_0_2213,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),zero_zero(X1)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1353]),
    [final] ).

cnf(i_0_2214,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),one_one(X1)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1354]),
    [final] ).

cnf(i_0_2215,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_1340]),
    [final] ).

cnf(i_0_2216,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_1340]),
    [final] ).

cnf(i_0_2217,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_1341]),
    [final] ).

cnf(i_0_2218,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_1341]),
    [final] ).

cnf(i_0_2219,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1355]),
    [final] ).

cnf(i_0_2220,plain,
    ( hBOOL(hAPP(nat,bool,X1,esk98_2(X2,X1)))
    | hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1240]),
    [final] ).

cnf(i_0_2221,plain,
    ( hBOOL(hAPP(nat,bool,X1,esk81_2(X2,X1)))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1208]),
    [final] ).

cnf(i_0_2222,plain,
    ( hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1355]),
    [final] ).

cnf(i_0_2223,plain,
    hAPP(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),combi(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3))),product_prod_rec(X1,X2,X3)) = product_prod_rec(X1,X2,X3),
    inference(rw,[status(thm)],[i_0_1356,c_0_839]),
    [final] ).

cnf(i_0_2224,plain,
    hAPP(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combi(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3)))),combc(X1,X2,X3)) = combc(X1,X2,X3),
    inference(rw,[status(thm)],[i_0_1357,c_0_839]),
    [final] ).

cnf(i_0_2225,plain,
    hAPP(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combi(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)))),combb(X1,X2,X3)) = combb(X1,X2,X3),
    inference(rw,[status(thm)],[i_0_1358,c_0_839]),
    [final] ).

cnf(i_0_2226,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1)))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1359]),
    [final] ).

cnf(i_0_2227,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1360]),
    [final] ).

cnf(i_0_2228,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_1340]),
    [final] ).

cnf(i_0_2229,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_1341]),
    [final] ).

cnf(i_0_2230,plain,
    hAPP(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),combi(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)))),hilbert_inv_into(X1,X2)) = hilbert_inv_into(X1,X2),
    inference(rw,[status(thm)],[i_0_1361,c_0_839]),
    [final] ).

cnf(i_0_2231,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1362]),
    [final] ).

cnf(i_0_2232,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),top_top(X1)))
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1363]),
    [final] ).

cnf(i_0_2233,plain,
    hAPP(fun(X1,bool),fun(sum_sum(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X1,bool),fun(sum_sum(X2,X1),bool)),sum_Plus(X2,X1),top_top(fun(X2,bool))),top_top(fun(X1,bool))) = top_top(fun(sum_sum(X2,X1),bool)),
    inference(split_conjunct,[status(thm)],[i_0_1364]),
    [final] ).

cnf(i_0_2234,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_1365]),
    [final] ).

cnf(i_0_2235,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1366]),
    [final] ).

cnf(i_0_2236,plain,
    ( X1 = zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1312]),
    [final] ).

cnf(i_0_2237,plain,
    ( X1 = zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1367]),
    [final] ).

cnf(i_0_2238,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1368]),
    [final] ).

cnf(i_0_2239,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1369]),
    [final] ).

cnf(i_0_2240,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1313]),
    [final] ).

cnf(i_0_2241,plain,
    hAPP(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combi(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)))),in_rel(X1,X2)) = in_rel(X1,X2),
    inference(rw,[status(thm)],[i_0_1370,c_0_839]),
    [final] ).

cnf(i_0_2242,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1232]),
    [final] ).

cnf(i_0_2243,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1229]),
    [final] ).

cnf(i_0_2244,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1371]),
    [final] ).

cnf(i_0_2245,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1372]),
    [final] ).

cnf(i_0_2246,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_1373]),
    [final] ).

cnf(i_0_2247,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1374]),
    [final] ).

cnf(i_0_2248,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1375]),
    [final] ).

cnf(i_0_2249,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1376]),
    [final] ).

cnf(i_0_2250,plain,
    hAPP(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),combi(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)))),image(X1,X2)) = image(X1,X2),
    inference(rw,[status(thm)],[i_0_1377,c_0_839]),
    [final] ).

cnf(i_0_2251,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1) ),
    inference(rw,[status(thm)],[i_0_1378,c_0_839]),
    [final] ).

cnf(i_0_2252,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | zero_zero(X1) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
    | ~ linord219039673up_add(X1) ),
    inference(rw,[status(thm)],[i_0_1379,c_0_839]),
    [final] ).

cnf(i_0_2253,plain,
    hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),combi(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    inference(rw,[status(thm)],[i_0_1380,c_0_839]),
    [final] ).

cnf(i_0_2254,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
    inference(rw,[status(thm)],[i_0_1381,c_0_839]),
    [final] ).

cnf(i_0_2255,plain,
    ( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1382,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2256,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_1340]),
    [final] ).

cnf(i_0_2257,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_1340]),
    [final] ).

cnf(i_0_2258,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_1341]),
    [final] ).

cnf(i_0_2259,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_1341]),
    [final] ).

cnf(i_0_2260,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
    inference(split_conjunct,[status(thm)],[fact_1_u]),
    [final] ).

cnf(i_0_2261,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
    inference(split_conjunct,[status(thm)],[fact_0_assms_I3_J]),
    [final] ).

cnf(i_0_2262,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_1383]),
    [final] ).

cnf(i_0_2263,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_1383]),
    [final] ).

cnf(i_0_2264,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_1384]),
    [final] ).

cnf(i_0_2265,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1) ),
    inference(rw,[status(thm)],[i_0_1385,c_0_839]),
    [final] ).

cnf(i_0_2266,plain,
    ( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1) ),
    inference(rw,[status(thm)],[i_0_1386,c_0_839]),
    [final] ).

cnf(i_0_2267,plain,
    hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3),X4) = hAPP(X1,X2,X3,X4),
    inference(rw,[status(thm)],[i_0_1387,c_0_839]),
    [final] ).

cnf(i_0_2268,plain,
    hAPP(fun(fun(X1,X2),fun(fun(X1,bool),bool)),fun(fun(X1,X2),fun(fun(X1,bool),bool)),combi(fun(fun(X1,X2),fun(fun(X1,bool),bool))),inj_on(X1,X2)) = inj_on(X1,X2),
    inference(rw,[status(thm)],[i_0_1388,c_0_839]),
    [final] ).

cnf(i_0_2269,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | one_one(nat) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1287]),
    [final] ).

cnf(i_0_2270,plain,
    hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = hAPP(X2,X2,combi(X2),X3),
    inference(rw,[status(thm)],[i_0_1389,c_0_839]),
    [final] ).

cnf(i_0_2271,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ comm_semiring_1(X1) ),
    inference(rw,[status(thm)],[i_0_1390,c_0_839]),
    [final] ).

cnf(i_0_2272,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ comm_monoid_add(X1) ),
    inference(rw,[status(thm)],[i_0_1391,c_0_839]),
    [final] ).

cnf(i_0_2273,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ monoid_add(X1) ),
    inference(rw,[status(thm)],[i_0_1392,c_0_839]),
    [final] ).

cnf(i_0_2274,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = hAPP(X1,X1,combi(X1),X2)
    | ~ comm_semiring_1(X1) ),
    inference(rw,[status(thm)],[i_0_1393,c_0_839]),
    [final] ).

cnf(i_0_2275,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = hAPP(X1,X1,combi(X1),X2)
    | ~ comm_monoid_add(X1) ),
    inference(rw,[status(thm)],[i_0_1394,c_0_839]),
    [final] ).

cnf(i_0_2276,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = hAPP(X1,X1,combi(X1),X2)
    | ~ monoid_add(X1) ),
    inference(rw,[status(thm)],[i_0_1395,c_0_839]),
    [final] ).

cnf(i_0_2277,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_1396]),
    [final] ).

cnf(i_0_2278,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_1397]),
    [final] ).

cnf(i_0_2279,plain,
    hAPP(nat,fun(nat,bool),ord_less(nat),X1) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),
    inference(split_conjunct,[status(thm)],[i_0_1398]),
    [final] ).

cnf(i_0_2280,plain,
    hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,product_prod(X1,X2))),combi(fun(X1,fun(X2,product_prod(X1,X2)))),product_Pair(X1,X2)) = product_Pair(X1,X2),
    inference(rw,[status(thm)],[i_0_1399,c_0_839]),
    [final] ).

cnf(i_0_2281,plain,
    hAPP(X1,X1,combi(X1),hAPP(X1,X1,combi(X1),X2)) = hAPP(X1,X1,combi(X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1400,c_0_839]),c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2282,plain,
    hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
    inference(rw,[status(thm)],[i_0_1401,c_0_839]),
    [final] ).

cnf(i_0_2283,plain,
    hAPP(X1,X1,combi(X1),hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    inference(rw,[status(thm)],[i_0_1402,c_0_839]),
    [final] ).

cnf(i_0_2284,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_1403]),
    [final] ).

cnf(i_0_2285,plain,
    hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(bool,fun(X1,fun(X1,X1))),combi(fun(bool,fun(X1,fun(X1,X1)))),if(X1)) = if(X1),
    inference(rw,[status(thm)],[i_0_1404,c_0_839]),
    [final] ).

cnf(i_0_2286,plain,
    ( hAPP(fun(X1,fun(X1,fun(X1,bool))),fun(X1,fun(X1,fun(X1,bool))),combi(fun(X1,fun(X1,fun(X1,bool)))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1)
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[i_0_1405,c_0_839]),
    [final] ).

cnf(i_0_2287,plain,
    hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(X1,fun(fun(X1,bool),bool)),combi(fun(X1,fun(fun(X1,bool),bool))),member(X1)) = member(X1),
    inference(rw,[status(thm)],[i_0_1406,c_0_839]),
    [final] ).

cnf(i_0_2288,plain,
    top_top(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fTrue)),
    inference(split_conjunct,[status(thm)],[i_0_1407]),
    [final] ).

cnf(i_0_2289,plain,
    hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),combi(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    inference(rw,[status(thm)],[i_0_1408,c_0_839]),
    [final] ).

cnf(i_0_2290,hypothesis,
    hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p) = p,
    inference(rw,[status(thm)],[i_0_1409,c_0_839]),
    [final] ).

cnf(i_0_2291,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1017]),
    [final] ).

cnf(i_0_2292,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_1410]),
    [final] ).

cnf(i_0_2293,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_1383]),
    [final] ).

cnf(i_0_2294,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1411]),
    [final] ).

cnf(i_0_2295,hypothesis,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) ),
    inference(rw,[status(thm)],[i_0_1412,c_0_839]),
    [final] ).

cnf(i_0_2296,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),zero_zero(nat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1413]),
    [final] ).

cnf(i_0_2297,plain,
    ( ~ hBOOL(hAPP(bool,bool,fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1414]),
    [final] ).

cnf(i_0_2298,plain,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1415]),
    [final] ).

cnf(i_0_2299,plain,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1416]),
    [final] ).

cnf(i_0_2300,plain,
    hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X1,bool),fun(X1,bool)),combi(fun(fun(X1,bool),fun(X1,bool))),collect(X1)) = collect(X1),
    inference(rw,[status(thm)],[i_0_1417,c_0_839]),
    [final] ).

cnf(i_0_2301,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1418]),
    [final] ).

cnf(i_0_2302,plain,
    hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
    inference(rw,[status(thm)],[i_0_1419,c_0_839]),
    [final] ).

cnf(i_0_2303,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[fact_277_finite__indi]),
    [final] ).

cnf(i_0_2304,plain,
    hAPP(fun(X1,fun(X2,X1)),fun(X1,fun(X2,X1)),combi(fun(X1,fun(X2,X1))),combk(X1,X2)) = combk(X1,X2),
    inference(rw,[status(thm)],[i_0_1420,c_0_839]),
    [final] ).

cnf(i_0_2305,plain,
    hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1421]),
    [final] ).

cnf(i_0_2306,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),plus_plus(X1)) = plus_plus(X1)
    | ~ cancel_semigroup_add(X1) ),
    inference(rw,[status(thm)],[i_0_1422,c_0_839]),
    [final] ).

cnf(i_0_2307,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),plus_plus(X1)) = plus_plus(X1)
    | ~ ab_semigroup_add(X1) ),
    inference(rw,[status(thm)],[i_0_1423,c_0_839]),
    [final] ).

cnf(i_0_2308,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),plus_plus(X1)) = plus_plus(X1)
    | ~ monoid_add(X1) ),
    inference(rw,[status(thm)],[i_0_1424,c_0_839]),
    [final] ).

cnf(i_0_2309,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1425]),
    [final] ).

cnf(i_0_2310,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1426]),
    [final] ).

cnf(i_0_2311,plain,
    ( hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combi(fun(X1,fun(X1,bool))),ord_less_eq(X1)) = ord_less_eq(X1)
    | ~ ord(X1) ),
    inference(rw,[status(thm)],[i_0_1427,c_0_839]),
    [final] ).

cnf(i_0_2312,plain,
    ( hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combi(fun(X1,fun(X1,bool))),ord_less(X1)) = ord_less(X1)
    | ~ ord(X1) ),
    inference(rw,[status(thm)],[i_0_1428,c_0_839]),
    [final] ).

cnf(i_0_2313,plain,
    hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combi(fun(X1,fun(X1,bool))),fequal(X1)) = fequal(X1),
    inference(rw,[status(thm)],[i_0_1429,c_0_839]),
    [final] ).

cnf(i_0_2314,plain,
    hAPP(fun(fun(X1,bool),nat),fun(fun(X1,bool),nat),combi(fun(fun(X1,bool),nat)),finite_card(X1)) = finite_card(X1),
    inference(rw,[status(thm)],[i_0_1430,c_0_839]),
    [final] ).

cnf(i_0_2315,plain,
    hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),combi(fun(fun(X1,bool),bool)),finite_finite_1(X1)) = finite_finite_1(X1),
    inference(rw,[status(thm)],[i_0_1431,c_0_839]),
    [final] ).

cnf(i_0_2316,hypothesis,
    ( hBOOL(hAPP(bool,bool,combi(bool),X1))
    | ~ hBOOL(X1) ),
    inference(rw,[status(thm)],[i_0_1432,c_0_839]),
    [final] ).

cnf(i_0_2317,plain,
    hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),combi(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba) = lba,
    inference(rw,[status(thm)],[i_0_1433,c_0_839]),
    [final] ).

cnf(i_0_2318,plain,
    hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),combi(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab) = lab,
    inference(rw,[status(thm)],[i_0_1434,c_0_839]),
    [final] ).

cnf(i_0_2319,plain,
    hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fdisj) = fdisj,
    inference(rw,[status(thm)],[i_0_1435,c_0_839]),
    [final] ).

cnf(i_0_2320,plain,
    hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fconj) = fconj,
    inference(rw,[status(thm)],[i_0_1436,c_0_839]),
    [final] ).

cnf(i_0_2321,plain,
    ( hAPP(bool,bool,combi(bool),X1) = fFalse
    | hAPP(bool,bool,combi(bool),X1) = fTrue ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1437,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2322,plain,
    ( hAPP(bool,bool,combi(bool),X1) = fFalse
    | hAPP(bool,bool,combi(bool),X1) = fTrue ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1438,c_0_839]),c_0_839]),
    [final] ).

cnf(i_0_2323,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(bool,bool,fNot,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1439]),
    [final] ).

cnf(i_0_2324,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[i_0_1440]),
    [final] ).

cnf(i_0_2325,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[i_0_1441]),
    [final] ).

cnf(i_0_2326,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[i_0_1442]),
    [final] ).

cnf(i_0_2327,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1443]),
    [final] ).

cnf(i_0_2328,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1444]),
    [final] ).

cnf(i_0_2329,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1445]),
    [final] ).

cnf(i_0_2330,plain,
    hAPP(nat,nat,suc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_1446]),
    [final] ).

cnf(i_0_2331,plain,
    X1 != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_1447]),
    [final] ).

cnf(i_0_2332,plain,
    hAPP(fun(X1,X1),fun(X1,X1),combi(fun(X1,X1)),combi(X1)) = combi(X1),
    inference(rw,[status(thm)],[i_0_1448,c_0_839]),
    [final] ).

cnf(i_0_2333,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),ring_1_Ints(X1)) = ring_1_Ints(X1)
    | ~ ring_1(X1) ),
    inference(rw,[status(thm)],[i_0_1449,c_0_839]),
    [final] ).

cnf(i_0_2334,plain,
    hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc) = suc,
    inference(rw,[status(thm)],[i_0_1450,c_0_839]),
    [final] ).

cnf(i_0_2335,plain,
    hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot) = fNot,
    inference(rw,[status(thm)],[i_0_1451,c_0_839]),
    [final] ).

cnf(i_0_2336,plain,
    hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,nat),combi(fun(arrow_660593299e_indi,nat)),h) = h,
    inference(rw,[status(thm)],[i_0_1452,c_0_839]),
    [final] ).

cnf(i_0_2337,plain,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    inference(split_conjunct,[status(thm)],[fact_288_card__UNIV__unit]),
    [final] ).

cnf(i_0_2338,plain,
    ( hAPP(X2,X1,top_top(fun(X2,X1)),X3) = top_top(X1)
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1453]),
    [final] ).

cnf(i_0_2339,plain,
    ( hAPP(X1,X1,combi(X1),top_top(X1)) = top_top(X1)
    | ~ top(X1) ),
    inference(rw,[status(thm)],[i_0_1454,c_0_839]),
    [final] ).

cnf(i_0_2340,plain,
    ( hAPP(X1,X1,combi(X1),zero_zero(X1)) = zero_zero(X1)
    | ~ zero(X1) ),
    inference(rw,[status(thm)],[i_0_1455,c_0_839]),
    [final] ).

cnf(i_0_2341,plain,
    ( hAPP(X1,X1,combi(X1),one_one(X1)) = one_one(X1)
    | ~ one(X1) ),
    inference(rw,[status(thm)],[i_0_1456,c_0_839]),
    [final] ).

cnf(i_0_2342,plain,
    hAPP(X1,X1,combi(X1),undefined(X1)) = undefined(X1),
    inference(rw,[status(thm)],[i_0_1457,c_0_839]),
    [final] ).

cnf(i_0_2343,plain,
    ( X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,esk96_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1458]),
    [final] ).

cnf(i_0_2344,plain,
    ( X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,esk95_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1459]),
    [final] ).

cnf(i_0_2345,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(split_conjunct,[status(thm)],[fact_402_One__nat__def]),
    [final] ).

cnf(i_0_2346,plain,
    hAPP(nat,nat,combi(nat),n) = n,
    inference(rw,[status(thm)],[i_0_1460,c_0_839]),
    [final] ).

cnf(i_0_2347,plain,
    hAPP(bool,bool,combi(bool),fTrue) = fTrue,
    inference(rw,[status(thm)],[i_0_1461,c_0_839]),
    [final] ).

cnf(i_0_2348,plain,
    hAPP(bool,bool,combi(bool),fFalse) = fFalse,
    inference(rw,[status(thm)],[i_0_1462,c_0_839]),
    [final] ).

cnf(i_0_2349,plain,
    hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),e) = e,
    inference(rw,[status(thm)],[i_0_1463,c_0_839]),
    [final] ).

cnf(i_0_2350,hypothesis,
    hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),d) = d,
    inference(rw,[status(thm)],[i_0_1464,c_0_839]),
    [final] ).

cnf(i_0_2351,hypothesis,
    hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),c) = c,
    inference(rw,[status(thm)],[i_0_1465,c_0_839]),
    [final] ).

cnf(i_0_2352,plain,
    hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),b) = b,
    inference(rw,[status(thm)],[i_0_1466,c_0_839]),
    [final] ).

cnf(i_0_2353,plain,
    hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),a) = a,
    inference(rw,[status(thm)],[i_0_1467,c_0_839]),
    [final] ).

cnf(i_0_2354,plain,
    ( finite_finite(sum_sum(X2,X1))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1468]),
    [final] ).

cnf(i_0_2355,plain,
    ( finite_finite(fun(X2,X1))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1469]),
    [final] ).

cnf(i_0_2356,plain,
    ( finite_finite(product_prod(X2,X1))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1470]),
    [final] ).

cnf(i_0_2357,plain,
    ( order(fun(X2,X1))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1471]),
    [final] ).

cnf(i_0_2358,plain,
    ( preorder(fun(X2,X1))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1472]),
    [final] ).

cnf(i_0_2359,plain,
    ( top(fun(X2,X1))
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1473]),
    [final] ).

cnf(i_0_2360,plain,
    ( ord(fun(X2,X1))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1474]),
    [final] ).

cnf(i_0_2361,plain,
    ( ~ zero_neq_one(X1)
    | one_one(X1) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1475]),
    [final] ).

cnf(i_0_2362,plain,
    ( ~ zero_neq_one(X1)
    | zero_zero(X1) != one_one(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1476]),
    [final] ).

cnf(i_0_2363,plain,
    ( finite_finite(option(X1))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1477]),
    [final] ).

cnf(i_0_2364,plain,
    comm_semiring_1(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring__1]),
    [final] ).

cnf(i_0_2365,plain,
    semiri456707255roduct(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc]),
    [final] ).

cnf(i_0_2366,plain,
    ordere216010020id_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__comm__monoid__add]),
    [final] ).

cnf(i_0_2367,plain,
    comm_monoid_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__add]),
    [final] ).

cnf(i_0_2368,plain,
    zero_neq_one(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ozero__neq__one]),
    [final] ).

cnf(i_0_2369,plain,
    finite_finite(product_unit),
    inference(split_conjunct,[status(thm)],[arity_Product__Type_Ounit___Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_2370,plain,
    finite_finite(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_2371,plain,
    ordere779506340up_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_2372,plain,
    ordere236663937imp_le(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le]),
    [final] ).

cnf(i_0_2373,plain,
    cancel146912293up_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_2374,plain,
    ordere223160158up_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_2375,plain,
    linordered_semidom(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_2376,plain,
    order(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]),
    [final] ).

cnf(i_0_2377,plain,
    order(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]),
    [final] ).

cnf(i_0_2378,plain,
    preorder(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]),
    [final] ).

cnf(i_0_2379,plain,
    preorder(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]),
    [final] ).

cnf(i_0_2380,plain,
    hBOOL(fTrue),
    inference(split_conjunct,[status(thm)],[help_fTrue_1_1_U]),
    [final] ).

cnf(i_0_2381,plain,
    linorder(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]),
    [final] ).

cnf(i_0_2382,plain,
    top(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Otop]),
    [final] ).

cnf(i_0_2383,plain,
    ord(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oord]),
    [final] ).

cnf(i_0_2384,plain,
    ord(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oord]),
    [final] ).

cnf(i_0_2385,plain,
    zero(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ozero]),
    [final] ).

cnf(i_0_2386,plain,
    cancel_semigroup_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__semigroup__add]),
    [final] ).

cnf(i_0_2387,plain,
    ab_semigroup_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__add]),
    [final] ).

cnf(i_0_2388,plain,
    monoid_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__add]),
    [final] ).

cnf(i_0_2389,plain,
    one(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oone]),
    [final] ).

cnf(i_0_2390,plain,
    c != d,
    inference(split_conjunct,[status(thm)],[fact_2__096c_A_126_061_Ad_096]),
    [final] ).

cnf(i_0_2391,plain,
    a != b,
    inference(split_conjunct,[status(thm)],[fact_36__096a_A_126_061_Ab_096]),
    [final] ).

cnf(i_0_2392,axiom,
    X1 = X1 ).

cnf(i_0_2393,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_2394,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_2395,axiom,
    ( X1 != X2
    | hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).

cnf(i_0_2396,axiom,
    ( X1 != X2
    | hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).

cnf(i_0_2397,axiom,
    ( X1 != X2
    | hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).

cnf(i_0_2398,axiom,
    ( X1 != X2
    | hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).

cnf(i_0_2399,axiom,
    ( X1 != X2
    | plus_plus(X1) = plus_plus(X2) ) ).

cnf(i_0_2400,axiom,
    ( X1 != X2
    | one_one(X1) = one_one(X2) ) ).

cnf(i_0_2401,axiom,
    ( X1 != X2
    | product_prod_rec(X1,X3,X4) = product_prod_rec(X2,X3,X4) ) ).

cnf(i_0_2402,axiom,
    ( X1 != X2
    | product_prod_rec(X3,X1,X4) = product_prod_rec(X3,X2,X4) ) ).

cnf(i_0_2403,axiom,
    ( X1 != X2
    | product_prod_rec(X3,X4,X1) = product_prod_rec(X3,X4,X2) ) ).

cnf(i_0_2404,axiom,
    ( X1 != X2
    | combs(X1,X3,X4) = combs(X2,X3,X4) ) ).

cnf(i_0_2405,axiom,
    ( X1 != X2
    | combs(X3,X1,X4) = combs(X3,X2,X4) ) ).

cnf(i_0_2406,axiom,
    ( X1 != X2
    | combs(X3,X4,X1) = combs(X3,X4,X2) ) ).

cnf(i_0_2407,axiom,
    ( X1 != X2
    | undefined(X1) = undefined(X2) ) ).

cnf(i_0_2408,axiom,
    ( X1 != X2
    | fequal(X1) = fequal(X2) ) ).

cnf(i_0_2409,axiom,
    ( X1 != X2
    | ord_less_eq(X1) = ord_less_eq(X2) ) ).

cnf(i_0_2410,axiom,
    ( X1 != X2
    | finite_card(X1) = finite_card(X2) ) ).

cnf(i_0_2411,axiom,
    ( X1 != X2
    | collect(X1) = collect(X2) ) ).

cnf(i_0_2412,axiom,
    ( X1 != X2
    | zero_zero(X1) = zero_zero(X2) ) ).

cnf(i_0_2413,axiom,
    ( X1 != X2
    | combi(X1) = combi(X2) ) ).

cnf(i_0_2414,axiom,
    ( X1 != X2
    | member(X1) = member(X2) ) ).

cnf(i_0_2415,axiom,
    ( X1 != X2
    | pi(X1,X3) = pi(X2,X3) ) ).

cnf(i_0_2416,axiom,
    ( X1 != X2
    | pi(X3,X1) = pi(X3,X2) ) ).

cnf(i_0_2417,axiom,
    ( X1 != X2
    | combk(X1,X3) = combk(X2,X3) ) ).

cnf(i_0_2418,axiom,
    ( X1 != X2
    | combk(X3,X1) = combk(X3,X2) ) ).

cnf(i_0_2419,axiom,
    ( X1 != X2
    | finite_finite_1(X1) = finite_finite_1(X2) ) ).

cnf(i_0_2420,axiom,
    ( X1 != X2
    | product_Pair(X1,X3) = product_Pair(X2,X3) ) ).

cnf(i_0_2421,axiom,
    ( X1 != X2
    | product_Pair(X3,X1) = product_Pair(X3,X2) ) ).

cnf(i_0_2422,axiom,
    ( X1 != X2
    | ring_1_Ints(X1) = ring_1_Ints(X2) ) ).

cnf(i_0_2423,axiom,
    ( X1 != X2
    | finite908156982e_idem(X1,X3) = finite908156982e_idem(X2,X3) ) ).

cnf(i_0_2424,axiom,
    ( X1 != X2
    | finite908156982e_idem(X3,X1) = finite908156982e_idem(X3,X2) ) ).

cnf(i_0_2425,axiom,
    ( X1 != X2
    | inj_on(X1,X3) = inj_on(X2,X3) ) ).

cnf(i_0_2426,axiom,
    ( X1 != X2
    | inj_on(X3,X1) = inj_on(X3,X2) ) ).

cnf(i_0_2427,axiom,
    ( X1 != X2
    | image(X1,X3) = image(X2,X3) ) ).

cnf(i_0_2428,axiom,
    ( X1 != X2
    | image(X3,X1) = image(X3,X2) ) ).

cnf(i_0_2429,axiom,
    ( X1 != X2
    | combc(X1,X3,X4) = combc(X2,X3,X4) ) ).

cnf(i_0_2430,axiom,
    ( X1 != X2
    | combc(X3,X1,X4) = combc(X3,X2,X4) ) ).

cnf(i_0_2431,axiom,
    ( X1 != X2
    | combc(X3,X4,X1) = combc(X3,X4,X2) ) ).

cnf(i_0_2432,axiom,
    ( X1 != X2
    | top_top(X1) = top_top(X2) ) ).

cnf(i_0_2433,axiom,
    ( X1 != X2
    | hilbert_inv_into(X1,X3) = hilbert_inv_into(X2,X3) ) ).

cnf(i_0_2434,axiom,
    ( X1 != X2
    | hilbert_inv_into(X3,X1) = hilbert_inv_into(X3,X2) ) ).

cnf(i_0_2435,axiom,
    ( X1 != X2
    | combb(X1,X3,X4) = combb(X2,X3,X4) ) ).

cnf(i_0_2436,axiom,
    ( X1 != X2
    | combb(X3,X1,X4) = combb(X3,X2,X4) ) ).

cnf(i_0_2437,axiom,
    ( X1 != X2
    | combb(X3,X4,X1) = combb(X3,X4,X2) ) ).

cnf(i_0_2438,axiom,
    ( X1 != X2
    | ord_atLeastLessThan(X1) = ord_atLeastLessThan(X2) ) ).

cnf(i_0_2439,axiom,
    ( X1 != X2
    | in_rel(X1,X3) = in_rel(X2,X3) ) ).

cnf(i_0_2440,axiom,
    ( X1 != X2
    | in_rel(X3,X1) = in_rel(X3,X2) ) ).

cnf(i_0_2441,axiom,
    ( X1 != X2
    | if(X1) = if(X2) ) ).

cnf(i_0_2442,axiom,
    ( X1 != X2
    | finite_fold_image(X1,X3) = finite_fold_image(X2,X3) ) ).

cnf(i_0_2443,axiom,
    ( X1 != X2
    | finite_fold_image(X3,X1) = finite_fold_image(X3,X2) ) ).

cnf(i_0_2444,axiom,
    ( X1 != X2
    | sum_Plus(X1,X3) = sum_Plus(X2,X3) ) ).

cnf(i_0_2445,axiom,
    ( X1 != X2
    | sum_Plus(X3,X1) = sum_Plus(X3,X2) ) ).

cnf(i_0_2446,axiom,
    ( X1 != X2
    | ord_less(X1) = ord_less(X2) ) ).

cnf(i_0_2447,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_2448,axiom,
    ( X1 != X2
    | ~ ring_1(X1)
    | ring_1(X2) ) ).

cnf(i_0_2449,axiom,
    ( X1 != X2
    | ~ ordere216010020id_add(X1)
    | ordere216010020id_add(X2) ) ).

cnf(i_0_2450,axiom,
    ( X1 != X2
    | ~ comm_semiring_1(X1)
    | comm_semiring_1(X2) ) ).

cnf(i_0_2451,axiom,
    ( X1 != X2
    | ~ linordered_semidom(X1)
    | linordered_semidom(X2) ) ).

cnf(i_0_2452,axiom,
    ( X1 != X2
    | ~ linordered_field(X1)
    | linordered_field(X2) ) ).

cnf(i_0_2453,axiom,
    ( X1 != X2
    | ~ dense_linorder(X1)
    | dense_linorder(X2) ) ).

cnf(i_0_2454,axiom,
    ( X1 != X2
    | ~ preorder(X1)
    | preorder(X2) ) ).

cnf(i_0_2455,axiom,
    ( X1 != X2
    | ~ ab_semigroup_add(X1)
    | ab_semigroup_add(X2) ) ).

cnf(i_0_2456,axiom,
    ( X1 != X2
    | ~ ring_char_0(X1)
    | ring_char_0(X2) ) ).

cnf(i_0_2457,axiom,
    ( X1 != X2
    | ~ cancel_semigroup_add(X1)
    | cancel_semigroup_add(X2) ) ).

cnf(i_0_2458,axiom,
    ( X1 != X2
    | ~ order(X1)
    | order(X2) ) ).

cnf(i_0_2459,axiom,
    ( X1 != X2
    | ~ cancel146912293up_add(X1)
    | cancel146912293up_add(X2) ) ).

cnf(i_0_2460,axiom,
    ( X1 != X2
    | ~ top(X1)
    | top(X2) ) ).

cnf(i_0_2461,axiom,
    ( X1 != X2
    | ~ semiri456707255roduct(X1)
    | semiri456707255roduct(X2) ) ).

cnf(i_0_2462,axiom,
    ( X1 != X2
    | ~ comm_monoid_add(X1)
    | comm_monoid_add(X2) ) ).

cnf(i_0_2463,axiom,
    ( X1 != X2
    | ~ monoid_add(X1)
    | monoid_add(X2) ) ).

cnf(i_0_2464,axiom,
    ( X1 != X2
    | ~ finite_finite(X1)
    | finite_finite(X2) ) ).

cnf(i_0_2465,axiom,
    ( X1 != X2
    | ~ zero(X1)
    | zero(X2) ) ).

cnf(i_0_2466,axiom,
    ( X1 != X2
    | ~ one(X1)
    | one(X2) ) ).

cnf(i_0_2467,axiom,
    ( X1 != X2
    | ~ zero_neq_one(X1)
    | zero_neq_one(X2) ) ).

cnf(i_0_2468,axiom,
    ( X1 != X2
    | ~ ord(X1)
    | ord(X2) ) ).

cnf(i_0_2469,axiom,
    ( X1 != X2
    | ~ linordered_idom(X1)
    | linordered_idom(X2) ) ).

cnf(i_0_2470,axiom,
    ( X1 != X2
    | ~ linorder(X1)
    | linorder(X2) ) ).

cnf(i_0_2471,axiom,
    ( X1 != X2
    | ~ ordere236663937imp_le(X1)
    | ordere236663937imp_le(X2) ) ).

cnf(i_0_2472,axiom,
    ( X1 != X2
    | ~ ordere779506340up_add(X1)
    | ordere779506340up_add(X2) ) ).

cnf(i_0_2473,axiom,
    ( X1 != X2
    | ~ ordere223160158up_add(X1)
    | ordere223160158up_add(X2) ) ).

cnf(i_0_2474,axiom,
    ( X1 != X2
    | ~ linord219039673up_add(X1)
    | linord219039673up_add(X2) ) ).

cnf(i_0_2392_001,axiom,
    X1 = X1 ).

cnf(i_0_2393_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_2394_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_2395_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).

cnf(i_0_2396_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).

cnf(i_0_2397_006,axiom,
    ( X1 != X2
    | hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).

cnf(i_0_2398_007,axiom,
    ( X1 != X2
    | hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).

cnf(i_0_2399_008,axiom,
    ( X1 != X2
    | plus_plus(X1) = plus_plus(X2) ) ).

cnf(i_0_2400_009,axiom,
    ( X1 != X2
    | one_one(X1) = one_one(X2) ) ).

cnf(i_0_2401_010,axiom,
    ( X1 != X2
    | product_prod_rec(X1,X3,X4) = product_prod_rec(X2,X3,X4) ) ).

cnf(i_0_2402_011,axiom,
    ( X1 != X2
    | product_prod_rec(X3,X1,X4) = product_prod_rec(X3,X2,X4) ) ).

cnf(i_0_2403_012,axiom,
    ( X1 != X2
    | product_prod_rec(X3,X4,X1) = product_prod_rec(X3,X4,X2) ) ).

cnf(i_0_2404_013,axiom,
    ( X1 != X2
    | combs(X1,X3,X4) = combs(X2,X3,X4) ) ).

cnf(i_0_2405_014,axiom,
    ( X1 != X2
    | combs(X3,X1,X4) = combs(X3,X2,X4) ) ).

cnf(i_0_2406_015,axiom,
    ( X1 != X2
    | combs(X3,X4,X1) = combs(X3,X4,X2) ) ).

cnf(i_0_2407_016,axiom,
    ( X1 != X2
    | undefined(X1) = undefined(X2) ) ).

cnf(i_0_2408_017,axiom,
    ( X1 != X2
    | fequal(X1) = fequal(X2) ) ).

cnf(i_0_2409_018,axiom,
    ( X1 != X2
    | ord_less_eq(X1) = ord_less_eq(X2) ) ).

cnf(i_0_2410_019,axiom,
    ( X1 != X2
    | finite_card(X1) = finite_card(X2) ) ).

cnf(i_0_2411_020,axiom,
    ( X1 != X2
    | collect(X1) = collect(X2) ) ).

cnf(i_0_2412_021,axiom,
    ( X1 != X2
    | zero_zero(X1) = zero_zero(X2) ) ).

cnf(i_0_2413_022,axiom,
    ( X1 != X2
    | combi(X1) = combi(X2) ) ).

cnf(i_0_2414_023,axiom,
    ( X1 != X2
    | member(X1) = member(X2) ) ).

cnf(i_0_2415_024,axiom,
    ( X1 != X2
    | pi(X1,X3) = pi(X2,X3) ) ).

cnf(i_0_2416_025,axiom,
    ( X1 != X2
    | pi(X3,X1) = pi(X3,X2) ) ).

cnf(i_0_2417_026,axiom,
    ( X1 != X2
    | combk(X1,X3) = combk(X2,X3) ) ).

cnf(i_0_2418_027,axiom,
    ( X1 != X2
    | combk(X3,X1) = combk(X3,X2) ) ).

cnf(i_0_2419_028,axiom,
    ( X1 != X2
    | finite_finite_1(X1) = finite_finite_1(X2) ) ).

cnf(i_0_2420_029,axiom,
    ( X1 != X2
    | product_Pair(X1,X3) = product_Pair(X2,X3) ) ).

cnf(i_0_2421_030,axiom,
    ( X1 != X2
    | product_Pair(X3,X1) = product_Pair(X3,X2) ) ).

cnf(i_0_2422_031,axiom,
    ( X1 != X2
    | ring_1_Ints(X1) = ring_1_Ints(X2) ) ).

cnf(i_0_2423_032,axiom,
    ( X1 != X2
    | finite908156982e_idem(X1,X3) = finite908156982e_idem(X2,X3) ) ).

cnf(i_0_2424_033,axiom,
    ( X1 != X2
    | finite908156982e_idem(X3,X1) = finite908156982e_idem(X3,X2) ) ).

cnf(i_0_2425_034,axiom,
    ( X1 != X2
    | inj_on(X1,X3) = inj_on(X2,X3) ) ).

cnf(i_0_2426_035,axiom,
    ( X1 != X2
    | inj_on(X3,X1) = inj_on(X3,X2) ) ).

cnf(i_0_2427_036,axiom,
    ( X1 != X2
    | image(X1,X3) = image(X2,X3) ) ).

cnf(i_0_2428_037,axiom,
    ( X1 != X2
    | image(X3,X1) = image(X3,X2) ) ).

cnf(i_0_2429_038,axiom,
    ( X1 != X2
    | combc(X1,X3,X4) = combc(X2,X3,X4) ) ).

cnf(i_0_2430_039,axiom,
    ( X1 != X2
    | combc(X3,X1,X4) = combc(X3,X2,X4) ) ).

cnf(i_0_2431_040,axiom,
    ( X1 != X2
    | combc(X3,X4,X1) = combc(X3,X4,X2) ) ).

cnf(i_0_2432_041,axiom,
    ( X1 != X2
    | top_top(X1) = top_top(X2) ) ).

cnf(i_0_2433_042,axiom,
    ( X1 != X2
    | hilbert_inv_into(X1,X3) = hilbert_inv_into(X2,X3) ) ).

cnf(i_0_2434_043,axiom,
    ( X1 != X2
    | hilbert_inv_into(X3,X1) = hilbert_inv_into(X3,X2) ) ).

cnf(i_0_2435_044,axiom,
    ( X1 != X2
    | combb(X1,X3,X4) = combb(X2,X3,X4) ) ).

cnf(i_0_2436_045,axiom,
    ( X1 != X2
    | combb(X3,X1,X4) = combb(X3,X2,X4) ) ).

cnf(i_0_2437_046,axiom,
    ( X1 != X2
    | combb(X3,X4,X1) = combb(X3,X4,X2) ) ).

cnf(i_0_2438_047,axiom,
    ( X1 != X2
    | ord_atLeastLessThan(X1) = ord_atLeastLessThan(X2) ) ).

cnf(i_0_2439_048,axiom,
    ( X1 != X2
    | in_rel(X1,X3) = in_rel(X2,X3) ) ).

cnf(i_0_2440_049,axiom,
    ( X1 != X2
    | in_rel(X3,X1) = in_rel(X3,X2) ) ).

cnf(i_0_2441_050,axiom,
    ( X1 != X2
    | if(X1) = if(X2) ) ).

cnf(i_0_2442_051,axiom,
    ( X1 != X2
    | finite_fold_image(X1,X3) = finite_fold_image(X2,X3) ) ).

cnf(i_0_2443_052,axiom,
    ( X1 != X2
    | finite_fold_image(X3,X1) = finite_fold_image(X3,X2) ) ).

cnf(i_0_2444_053,axiom,
    ( X1 != X2
    | sum_Plus(X1,X3) = sum_Plus(X2,X3) ) ).

cnf(i_0_2445_054,axiom,
    ( X1 != X2
    | sum_Plus(X3,X1) = sum_Plus(X3,X2) ) ).

cnf(i_0_2446_055,axiom,
    ( X1 != X2
    | ord_less(X1) = ord_less(X2) ) ).

cnf(i_0_2447_056,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_2448_057,axiom,
    ( X1 != X2
    | ~ ring_1(X1)
    | ring_1(X2) ) ).

cnf(i_0_2449_058,axiom,
    ( X1 != X2
    | ~ ordere216010020id_add(X1)
    | ordere216010020id_add(X2) ) ).

cnf(i_0_2450_059,axiom,
    ( X1 != X2
    | ~ comm_semiring_1(X1)
    | comm_semiring_1(X2) ) ).

cnf(i_0_2451_060,axiom,
    ( X1 != X2
    | ~ linordered_semidom(X1)
    | linordered_semidom(X2) ) ).

cnf(i_0_2452_061,axiom,
    ( X1 != X2
    | ~ linordered_field(X1)
    | linordered_field(X2) ) ).

cnf(i_0_2453_062,axiom,
    ( X1 != X2
    | ~ dense_linorder(X1)
    | dense_linorder(X2) ) ).

cnf(i_0_2454_063,axiom,
    ( X1 != X2
    | ~ preorder(X1)
    | preorder(X2) ) ).

cnf(i_0_2455_064,axiom,
    ( X1 != X2
    | ~ ab_semigroup_add(X1)
    | ab_semigroup_add(X2) ) ).

cnf(i_0_2456_065,axiom,
    ( X1 != X2
    | ~ ring_char_0(X1)
    | ring_char_0(X2) ) ).

cnf(i_0_2457_066,axiom,
    ( X1 != X2
    | ~ cancel_semigroup_add(X1)
    | cancel_semigroup_add(X2) ) ).

cnf(i_0_2458_067,axiom,
    ( X1 != X2
    | ~ order(X1)
    | order(X2) ) ).

cnf(i_0_2459_068,axiom,
    ( X1 != X2
    | ~ cancel146912293up_add(X1)
    | cancel146912293up_add(X2) ) ).

cnf(i_0_2460_069,axiom,
    ( X1 != X2
    | ~ top(X1)
    | top(X2) ) ).

cnf(i_0_2461_070,axiom,
    ( X1 != X2
    | ~ semiri456707255roduct(X1)
    | semiri456707255roduct(X2) ) ).

cnf(i_0_2462_071,axiom,
    ( X1 != X2
    | ~ comm_monoid_add(X1)
    | comm_monoid_add(X2) ) ).

cnf(i_0_2463_072,axiom,
    ( X1 != X2
    | ~ monoid_add(X1)
    | monoid_add(X2) ) ).

cnf(i_0_2464_073,axiom,
    ( X1 != X2
    | ~ finite_finite(X1)
    | finite_finite(X2) ) ).

cnf(i_0_2465_074,axiom,
    ( X1 != X2
    | ~ zero(X1)
    | zero(X2) ) ).

cnf(i_0_2466_075,axiom,
    ( X1 != X2
    | ~ one(X1)
    | one(X2) ) ).

cnf(i_0_2467_076,axiom,
    ( X1 != X2
    | ~ zero_neq_one(X1)
    | zero_neq_one(X2) ) ).

cnf(i_0_2468_077,axiom,
    ( X1 != X2
    | ~ ord(X1)
    | ord(X2) ) ).

cnf(i_0_2469_078,axiom,
    ( X1 != X2
    | ~ linordered_idom(X1)
    | linordered_idom(X2) ) ).

cnf(i_0_2470_079,axiom,
    ( X1 != X2
    | ~ linorder(X1)
    | linorder(X2) ) ).

cnf(i_0_2471_080,axiom,
    ( X1 != X2
    | ~ ordere236663937imp_le(X1)
    | ordere236663937imp_le(X2) ) ).

cnf(i_0_2472_081,axiom,
    ( X1 != X2
    | ~ ordere779506340up_add(X1)
    | ordere779506340up_add(X2) ) ).

cnf(i_0_2473_082,axiom,
    ( X1 != X2
    | ~ ordere223160158up_add(X1)
    | ordere223160158up_add(X2) ) ).

cnf(i_0_2474_083,axiom,
    ( X1 != X2
    | ~ linord219039673up_add(X1)
    | linord219039673up_add(X2) ) ).

cnf(i_0_2475,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X1),X2))) ),
    inference(equality_inference,[],[1582]) ).

cnf(i_0_2476,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X2),X1))) ),
    inference(equality_inference,[],[1583]) ).

cnf(i_0_2477,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X2),X1))) ),
    inference(equality_inference,[],[1584]) ).

cnf(i_0_2478,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X1),X2))) ),
    inference(equality_inference,[],[1585]) ).

cnf(i_0_2479,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X3),X1))) ),
    inference(equality_inference,[],[1597]) ).

cnf(i_0_2480,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X1),X3))) ),
    inference(equality_inference,[],[1598]) ).

cnf(i_0_2481,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X2),X1))) ),
    inference(equality_inference,[],[1603]) ).

cnf(i_0_2482,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X1),X2))) ),
    inference(equality_inference,[],[1604]) ).

cnf(i_0_2483,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X3),X1))) ),
    inference(equality_inference,[],[1619]) ).

cnf(i_0_2484,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X1),X2))) ),
    inference(equality_inference,[],[1620]) ).

cnf(i_0_2485,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X1),X2))) ),
    inference(equality_inference,[],[1621]) ).

cnf(i_0_2486,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X2),X1))) ),
    inference(equality_inference,[],[1622]) ).

cnf(i_0_2487,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X3)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X4),X2),X1))) ),
    inference(equality_inference,[],[1626]) ).

cnf(i_0_2488,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X4),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X4),X1),X2))) ),
    inference(equality_inference,[],[1627]) ).

cnf(i_0_2489,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2))) ),
    inference(equality_inference,[],[1633]) ).

cnf(i_0_2490,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X4)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2))) ),
    inference(equality_inference,[],[1634]) ).

cnf(i_0_2491,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(equality_inference,[],[1676]) ).

cnf(i_0_2492,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X1))),
    inference(equality_inference,[],[1686]) ).

cnf(i_0_2493,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X2))),
    inference(equality_inference,[],[1687]) ).

cnf(i_0_2494,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X1))) ),
    inference(equality_inference,[],[1725]) ).

cnf(i_0_2495,plain,
    ( hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X1) = hAPP(arrow_490897120le_alt,arrow_490897120le_alt,combi(arrow_490897120le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X1))) ),
    inference(equality_inference,[],[1726]) ).

cnf(i_0_2496,plain,
    ( hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X5)) ),
    inference(equality_inference,[],[1794]) ).

cnf(i_0_2497,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X5)) ),
    inference(equality_inference,[],[1798]) ).

cnf(i_0_2498,plain,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X3))) ),
    inference(equality_inference,[],[1802]) ).

cnf(i_0_2499,plain,
    ( hAPP(X1,X1,hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,bool),fun(fun(X1,X1),fun(X1,X1)),hilbert_inv_into(X1,X1),X2),combi(X1)),X3) = hAPP(X1,X1,combi(X1),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
    inference(equality_inference,[],[1820]) ).

cnf(i_0_2500,plain,
    ( ~ linorder(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(equality_inference,[],[1843]) ).

cnf(i_0_2501,plain,
    ( ~ linorder(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(equality_inference,[],[1844]) ).

cnf(i_0_2502,plain,
    ( ~ linorder(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(equality_inference,[],[1845]) ).

cnf(i_0_2503,plain,
    ( ~ linorder(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(equality_inference,[],[1846]) ).

cnf(i_0_2504,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),top_top(fun(X1,bool))))),
    inference(equality_inference,[],[1869]) ).

cnf(i_0_2505,plain,
    ( hAPP(X1,X1,hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,bool),fun(fun(X1,X1),fun(X1,X1)),hilbert_inv_into(X1,X1),top_top(fun(X1,bool))),combi(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),top_top(fun(X1,bool)))) ),
    inference(equality_inference,[],[1886]) ).

cnf(i_0_2506,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(equality_inference,[],[1960]) ).

cnf(i_0_2507,plain,
    ( hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(equality_inference,[],[2013]) ).

cnf(i_0_2508,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),top_top(fun(X1,bool)))) ),
    inference(equality_inference,[],[2015]) ).

cnf(i_0_2509,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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,[],[2023]) ).

cnf(i_0_2510,plain,
    ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X2)),
    inference(equality_inference,[],[2024]) ).

cnf(i_0_2511,plain,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
    inference(equality_inference,[],[2054]) ).

cnf(i_0_2512,plain,
    hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2),
    inference(equality_inference,[],[2077]) ).

cnf(i_0_2513,plain,
    hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2),
    inference(equality_inference,[],[2079]) ).

cnf(i_0_2514,plain,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
    inference(equality_inference,[],[2091]) ).

cnf(i_0_2515,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
    inference(equality_inference,[],[2094]) ).

cnf(i_0_2516,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
    inference(equality_inference,[],[2110]) ).

cnf(i_0_2517,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
    inference(equality_inference,[],[2111]) ).

cnf(i_0_2518,plain,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
    inference(equality_inference,[],[2124]) ).

cnf(i_0_2519,plain,
    ( ~ cancel146912293up_add(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
    inference(equality_inference,[],[2125]) ).

cnf(i_0_2520,plain,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
    inference(equality_inference,[],[2127]) ).

cnf(i_0_2521,plain,
    hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3) = hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3),
    inference(equality_inference,[],[2128]) ).

cnf(i_0_2522,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))),
    inference(equality_inference,[],[2143]) ).

cnf(i_0_2523,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
    inference(equality_inference,[],[2156]) ).

cnf(i_0_2524,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
    inference(equality_inference,[],[2157]) ).

cnf(i_0_2525,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(equality_inference,[],[2165]) ).

cnf(i_0_2526,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(equality_inference,[],[2169]) ).

cnf(i_0_2527,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(equality_inference,[],[2170]) ).

cnf(i_0_2528,plain,
    X1 = X1,
    inference(equality_inference,[],[2173]) ).

cnf(i_0_2529,plain,
    X1 = X1,
    inference(equality_inference,[],[2174]) ).

cnf(i_0_2530,plain,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) ),
    inference(equality_inference,[],[2181]) ).

cnf(i_0_2531,plain,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) ),
    inference(equality_inference,[],[2182]) ).

cnf(i_0_2532,plain,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
    inference(equality_inference,[],[2185]) ).

cnf(i_0_2533,plain,
    hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2)),
    inference(equality_inference,[],[2186]) ).

cnf(i_0_2534,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),top_top(fun(X1,bool))) = top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(equality_inference,[],[2190]) ).

cnf(i_0_2535,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
    inference(equality_inference,[],[2207]) ).

cnf(i_0_2536,plain,
    ( ~ preorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
    inference(equality_inference,[],[2234]) ).

cnf(i_0_2537,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
    inference(equality_inference,[],[2244]) ).

cnf(i_0_2538,plain,
    X1 = X1,
    inference(equality_inference,[],[2299]) ).

cnf(i_0_2539,plain,
    $false,
    inference(scs_inference,[],[i_0_1720,i_0_1486,i_0_1480]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SCT171+6 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33  % Computer : n010.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Tue May  5 02:01:51 EDT 2026
% 0.16/0.34  % CPUTime    : 
% 0.16/0.35  % start to proof: theBenchmark
% 1.91/1.85  % Version  : CSE_E---1.7
% 1.91/1.85  % Problem  : theBenchmark.p
% 1.91/1.85  % SZS status Theorem for theBenchmark.p
% 1.91/1.85  % SZS output start CNFRefutation
% See solution above
% 1.98/1.95  % Total time : 1.494s
%------------------------------------------------------------------------------